Apparatus for controlling rotational speed of internal combustion engine

ABSTRACT

A control apparatus controls the rotational speed of an internal combustion engine by generating a command value for ignition timing of the internal combustion engine to convert an actual rotational speed of the internal combustion engine to a predetermined target rotational speed according to a feedback control process and controlling the ignition timing based on the generated command value. The feedback control process is carried out by a response designating control process capable of variably designating a rate of reduction of the difference between the actual rotational speed of the internal combustion engine and the target rotational speed with the value of a predetermined parameter in the feedback control process. The value of the predetermined parameter is variably established under a predetermined condition.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an apparatus for controlling therotational speed of an internal combustion engine at a predeterminedtarget rotational speed according to a feedback control process bycontrolling the ignition timing of the internal combustion engine.

2. Description of the Related Art

It is the general practice to control the actual rotational speed of aninternal combustion engine at a predetermined target rotational speedaccording to a feedback control process, e.g., while the internalcombustion engine is operating in an idling mode, by controlling theamount of intake air introduced into the internal combustion engine. Theactual rotational speed of the internal combustion engine can also beadjusted by controlling the ignition timing of the internal combustionengine. Specifically, if the amount of intake air is constant, then asthe ignition timing is more retarded, the actual rotational speed of theinternal combustion engine is reduced, and as the ignition timing ismore advanced, the actual rotational speed of the internal combustionengine is increased. Accordingly, the ignition timing may be controlledto converge the actual rotational speed of the internal combustionengine to a desired target rotational speed according to a feedbackcontrol process.

The applicant of the present application has proposed the followingtechnique in Japanese laid-open patent publication No. 10-299631,Japanese laid-open patent Publication No. 11-210608, and U.S. patentapplication No. 09/063732, for example.

According to the disclosed technique, in order to quickly increase thetemperature of and activate a catalytic converter disposed in theexhaust system of an internal combustion engine while the internalcombustion engine is idling after it has started to operate, the amountof intake air introduced into the internal combustion engine isincreased to a level greater than while the internal combustion engineis idling, for thereby increasing the amount of heat energy of exhaustgases that are emitted from the internal combustion engine when theair-fuel mixture is combusted in a combustion chamber of the internalcombustion engine. A command value for the ignition timing of theinternal combustion engine is generated according to a feedback controlprocess using a PI (proportional plus integral) control process in orderto converge the actual rotational speed of the internal combustionengine, which tends to increase due to the increased amount of intakeair, to an optimum idling rotational speed. Based on the generatedcommand value, the ignition timing of the internal combustion engine iscontrolled to control the actual rotational speed of the internalcombustion engine at the desired idling rotational speed.

Various studies made by the inventors of the present application haverevealed that when the ignition timing of the internal combustion engineis controlled to control the actual rotational speed of the internalcombustion engine at the target idling rotational speed according to afeedback control process (hereinafter referred to as an “ignition timingcontrol rotational speed F/B control process”), the ignition timing hasa relatively large effect on the combustion status of the air-fuelmixture in the internal combustion engine and the behavioralcharacteristics of the internal combustion engine. Therefore, it ishighly necessary to accurately control the ignition timing in a mannerto match operating conditions of the internal combustion engine,depending on the difference (hereinafter referred to as a “rotationalspeed difference”) between the actual rotational speed of the internalcombustion engine and target idling rotational speed.

For example, the rate of a change of the actual rotational speed of theinternal combustion engine to a change of the ignition timing tends tobe greater as the ignition timing is more retarded. Therefore, when theignition timing of the internal combustion engine is relatively largelyretarded, if a change of the ignition timing (a corrective quantity ofthe ignition timing) dependent on the rotational speed differenceaccording to the ignition timing control rotational speed F/B controlprocess is excessively large, meaning that the feedback gain of theignition timing control rotational speed F/B control process isexcessively large, then the actual rotational speed excessively changesto the target rotational speed, meaning that the rate of reduction ofthe rotational speed difference is excessively large, and the actualrotational speed is liable to be unstable (the actual rotational speedis liable to fluctuate in an oscillatory fashion with respect to thetarget rotational speed).

Conversely, when the ignition timing of the internal combustion engineis controlled to be advanced, if a change of the ignition timingdependent on the rotational speed difference is excessively small, i.e.,the feedback gain is excessively small, then the rate of reduction ofthe rotational speed difference becomes much small so that the actualrotational speed cannot be converged quickly to the target rotationalspeed.

For example, if the ignition timing is advanced, if the ignition timingcontrol rotational speed F/B control process is performed while theinternal combustion engine is idling after it has started to operate,then in an initial stage of operation in which the ignition timingcontrol rotational speed F/B control process is carried out, i.e.,immediately after the internal combustion engine has started to operate,the combustion status of the internal combustion engine is apt to beunstable. Therefore, abruptly changing the ignition timing in order toconverge the actual rotational speed to the target rotational speedcauses the combustion and emission statuses of the internal combustionengine to be impaired and makes the operating conditions of the internalcombustion engine unstable.

In view of the foregoing, if the ignition timing control rotationalspeed F/B control process is carried out according to a PI controlprocess as proposed in the above technique by the applicant, then it ispreferable to variably establish a proportional gain and an integralgain (coefficients relative to proportional and integral terms of the PIcontrol process) which defines the feedback gain of the PI controlprocess, depending on required conditions such as the operatingconditions of the internal combustion engine.

According to the PI control process, however, when a command value forthe ignition timing depending on the rotational speed difference isdetermined by the processing of the PI control process, and the ignitiontiming is controlled by the command value, it is generally difficult topredict behaviors with which the actual rotational speed of the internalcombustion engine is converged to the target rotational speed. Statedotherwise, if the actual rotational speed is to be converged to thetarget rotational speed in a desired behavioral manner, it is difficultto predict what values the proportional and integral gains should haveto achieve the desired behavioral manner.

Therefore, the values of the proportional and integral gains, which areto be established depending on the operating conditions of the internalcombustion engine, have to be determined in a trial-and-error fashionvia various experiments or the like. The determination of the values ofthe proportional and integral gains thus needs a large expenditure oflabor, and it is difficult to determine the values of the proportionaland integral gains finely and accurately depending on various operatingconditions of the internal combustion engine.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide anapparatus for controlling the actual rotational speed of an internalcombustion engine at a target rotational speed according to a feedbackcontrol process by controlling the ignition timing of the internalcombustion engine appropriately under various operating conditions ofthe internal combustion engine, in view of the stability of the feedbackcontrol process and the operating conditions of the internal combustionengine, and allowing a system for the feedback control process to beeasily constructed.

In order to achieve the above object, there is provided in accordancewith the present invention an apparatus for controlling the rotationalspeed of an internal combustion engine by generating a command value forignition timing of the internal combustion engine to convert an actualrotational speed of the internal combustion engine to a predeterminedtarget rotational speed according to a feedback control process andcontrolling the ignition timing based on the generated command value,wherein the feedback control process is carried out by a responsedesignating control process capable of variably designating a rate ofreduction of the difference between the actual rotational speed of theinternal combustion engine and the target rotational speed with thevalue of a predetermined parameter in the feedback control process, andthe value of the predetermined parameter is variably established under apredetermined condition.

With the above arrangement, the feedback control process is carried outby a response designating control process capable of variablydesignating a rate of reduction (the degree of a time-dependent change)of the difference between the actual rotational speed of the internalcombustion engine and the target rotational speed (more generally thedifference between a control quantity of an object to the controlled anda target value thereof) with the value of a predetermined parameter inthe feedback control process. When the ignition timing of the internalcombustion engine is controlled on the basis of the command value forthe ignition timing generated by the feedback control process accordingto the response designating control process, a behavioral manner inwhich the actual rotational speed of the internal combustion engine isconverged to the target rotational speed is defined by the value of thepredetermined parameter. Therefore, the behavioral manner in which theactual rotational speed of the internal combustion engine is convergedto the target rotational speed can be designated directly by the valueof the predetermined parameter. By variably establishing the value ofthe predetermined parameter under a suitable condition, the actualrotational speed of the internal combustion engine can befeedback-controlled at the target rotational speed by controlling theignition timing accurately under various operating conditions of theinternal combustion engine in view of the stability of the feedbackcontrol process and the stability of the operating conditions of theinternal combustion engine. Since the rate of reduction of thedifference between the actual rotational speed and the target rotationalspeed, i.e., the behavioral manner in which the actual rotational speedof the internal combustion engine is converged to the target rotationalspeed, can directly be designated by the value of the parameter, asystem of the rotational speed control apparatus according to thepresent invention can easily be constructed.

Increasing the rate of reduction of the difference is equivalent toincreasing the feedback gain, and reducing the rate of reduction of thedifference is equivalent to reducing the feedback gain.

Specifically, the predetermined condition for variably establishing thevalue of the predetermined parameter may include the ignition timing ofthe internal combustion engine controlled based on the command value forthe ignition timing, the value of the predetermined parameter beingestablished such that as the ignition timing is more retarded, the rateof reduction of the difference between the actual rotational speed ofthe internal combustion engine and the target rotational speed issmaller.

When the ignition timing of the internal combustion engine is largelyretarded, a change in the rotational speed of the internal combustionengine tends to be large with respect to a change in the ignitiontiming. According to the present invention, when the value of thepredetermined parameter is established such that as the ignition timingis more retarded, the rate of reduction is smaller, the feedback gain issmaller as the ignition timing is more retarded. Therefore, when theactual rotational speed of the internal combustion engine differs to acertain extent from the target rotational speed, a change in theignition timing of the internal combustion engine generated based on thecommand value for the ignition timing according to the feedback controlprocess is smaller as the ignition timing is more retarded. As a result,the actual rotational speed of the internal combustion engine isprevented from being abruptly converged to the target rotational speed,and the actual rotational speed can be converged stably to the targetrotational speed.

Conversely, when the ignition timing of the internal combustion engineis more advanced, a change in the rotational speed of the internalcombustion engine tends to be smaller with respect to a change in theignition timing. According to the present invention, when the actualrotational speed of the internal combustion engine differs to a certainextent from the target rotational speed, a change in the ignition timingof the internal combustion engine generated based on the command valuefor the ignition timing according to the feedback control process isgreater as the ignition timing is more advanced. As a result, the actualrotational speed of the internal combustion engine can be convergedquickly to the target rotational speed.

Thus, the feedback control process for converging the actual rotationalspeed to the target rotational speed can stably and smoothly be carriedout irrespective of the retarded/advanced state of the ignition timing.

The predetermined condition for variably establishing the value of thepredetermined parameter may include the actual rotational speed of theinternal combustion engine, the value of the predetermined parameterbeing established such that as the actual rotational speed is moredifferent from the target rotational speed, the rate of reduction of thedifference between the actual rotational speed of the internalcombustion engine and the target rotational speed is smaller.

When the actual rotational speed differs relatively largely from thetarget rotational speed due to disturbance or the like, i.e., when thedifference between the actual and target rotational speeds becomeslarger, the command value for the ignition timing is basically generatedaccording to the feedback control process to change the ignition timingrelatively largely in order to eliminate the difference between theactual rotational speed and the target rotational speed. If the ignitiontiming abruptly changes, then the combustion status of the internalcombustion engine tends to be unstable. According to the presentinvention, the value of the predetermined parameter is established suchthat as the actual rotational speed is more different from the targetrotational speed, the rate of reduction of the difference is smaller.Therefore, the command value is generated to suppress an abrupt changein the ignition timing when the actual rotational speed differsrelatively greatly from the target rotational speed, allowing theinternal combustion engine to operate in stable operating conditions.

The ignition timing of the internal combustion engine may be controlledbased on the command value for the ignition timing which is generated bythe feedback control process, immediately after the internal combustionengine has started to operate while the internal combustion engine isidling, and the predetermined condition for variably establishing thevalue of the predetermined parameter may include a time which haselapsed after the ignition timing has started to be controlled by thecommand value, the value of the predetermined parameter beingestablished such that until the elapsed time reaches a predeterminedvalue, the rate of reduction of the difference between the actualrotational speed of the internal combustion engine and the targetrotational speed is smaller than after the elapsed time has reached thepredetermined value.

In an initial stage after the internal combustion engine has started tooperate, the combustion status of the internal combustion engine tendsto be unstable. According to the present invention, the value of thepredetermined parameter is established such that until the time whichhas elapsed after the ignition timing has started to be controlled bythe command value reaches the predetermined value, the rate of reductionof the difference is small. Therefore, an abrupt change in the ignitiontiming dependent on the different is avoided, and the internalcombustion engine operates in stable operating conditions.

The apparatus may comprise amount-of-intake-air control means forcontrolling the amount of intake air introduced into the internalcombustion engine to converge a control quantity, other than the actualrotational speed, of the internal combustion engine to a predeterminedtarget value according to a feedback control process, concurrent withcontrolling the ignition timing of the internal combustion engine basedon the command value for the ignition timing which is generated by thefeedback control process, the value of the predetermined parameter beingestablished such that the rate of reduction of the difference betweenthe actual rotational speed of the internal combustion engine and thetarget rotational speed according to the response designating controlprocess is greater than the rate of reduction of the difference betweenthe control quantity and the target value according to the feedbackcontrol process of the amount-of-intake-air control means.

With the amount-of-intake-air control means added, in addition to thefeedback control process for controlling the actual rotational speed ofthe internal combustion engine, the amount of intake air introduced intothe internal combustion engine is controlled in order to converge agiven control quantity, other than the actual rotational speed of theinternal combustion engine, e.g., an integrated value of the amount ofintake air, an amount of heat energy of exhaust gases, and an outputtorque, to a predetermined target value. Controlling the amount ofintake air affects the actual rotational speed of the internalcombustion engine. Generally, the response of a change in the actualrotational speed of the internal combustion engine with respect to achange in the amount of intake air is slower than the response of achange in the actual rotational speed of the internal combustion enginewith respect to a change in the ignition timing.

Therefore, if the value of the predetermined parameter is establishedsuch that the rate of reduction of the difference between the actual andtarget rotational speeds according to the response designating controlprocess is smaller than the rate of reduction of the difference betweenthe control quantity and the target value according to the feedbackcontrol process of the amount-of-intake-air control means, i.e., thefeedback gain of the response designating control process is smallerthan the feedback gain of the amount-of-intake-air control means, thenthe feed-back control process based on controlling the amount of intakeair and the feedback control process based on controlling the ignitiontiming may interfere with each other, possibly making the actualrotational speed of the internal combustion engine unstable.

According to the present invention, the rate of reduction of thedifference between the actual and target rotational speeds according tothe response designating control process is made greater than the rateof reduction of the difference between the control quantity and thetarget value according to the feedback control process of theamount-of-intake-air control means. This arrangement is effective toavoid the above drawbacks, and control the actual rotational speed ofthe-internal combustion engine at the target rotational speed.

The response designating control process needs a suitable model of theobject to be controlled in order to perform its processing operation.The model may be constructed of either a continuous system(specifically, a continuous-time system) or a discrete system(specifically, a discrete-time system). If the model is constructed of acontinuous system, then when the control processing of the responsedesignating control process is performed by a computer handlingdiscrete-time data, an algorithm of the control processing tends to becomplex.

According to the present invention, the response designating controlprocess has an object to be controlled which is handled as a system forgenerating data representing the actual rotational speed of the internalcombustion engine from data representing the command value for theignition timing, and carries out the feedback control process in apredetermined control cycle based on a discrete system model whichrepresents a model of the object to be controlled as a discrete system.

As described above, the object to be controlled by the responsedesignating control process is modeled as a discrete system, and thefeedback control process, i.e., a process of determining the commandvalue for the ignition timing of the internal combustion engine in orderto converge the actual rotational speed of the internal combustionengine to the target value, is carried out on the basis of thediscrete-system model. Therefore, the algorithm of the controlprocessing can be simplified for computer processing. With the object tobe controlled being modeled as a discrete system, the value of aparameter of the model which is to be established to determine the modelcan easily be determined using a known identifying algorithm.

In the case where the object to be controlled by the responsedesignating control process is modeled as a discrete system, the datarepresenting the actual rotational speed of the internal combustionengine in each control cycle of the response designating control processis preferably expressed by data representing the actual rotational speedof the internal combustion engine in a control cycle prior to thecontrol cycle and data representing the command value for the ignitiontiming.

The above modeling scheme allows behaviors of the object to becontrolled by the response designating control process, i.e., a systemfor generating the data representing the actual rotational speed of theinternal combustion engine from the data representing the command valuefor the ignition timing, to be expressed accurately and simply by thediscrete-system model.

In the case where the object to be controlled by the responsedesignating control process is modeled as a discrete system, the datarepresenting the command value for the ignition timing comprises thedifference between the command value for the ignition timing and apredetermined reference command value, and the data representing theactual rotational speed of the internal combustion engine preferablycomprises the difference between the actual rotational speed and apredetermined reference rotational speed.

With the above arrangement, the discrete-system model and an algorithmof the processing of the feedback control process according to theresponse designating control process can easily be constructed.

The response designating control process includes a sliding mode controlprocess, an ILQ control process (response designating adaptive controlprocess), etc. However, the response designating control process shouldpreferably comprise a sliding mode control process, which shouldpreferably comprise an adaptive sliding mode control process.

The sliding mode control process is a variable-structure-type feedbackcontrol process having such general characteristics that its controlstability with respect to disturbance and modeling errors is high.Particularly, the adaptive sliding mode control process positivelyeliminates the effect of disturbance and modeling errors by adding acontrol law referred to as an adaptive law (adaptive algorithm) to thenormal sliding mode control process.

Therefore, if the response designating control process comprises asliding mode control process, and more preferably an adaptive slidingmode control process, then the actual rotational speed of the internalcombustion engine can highly stably be converged to the targetrotational speed.

With the sliding mode control process used as the response designatingcontrol process, the predetermined parameter is a coefficient parameterof a linear switching function used in the sliding mode control process.

Specifically, the sliding mode control process employs a function knownas a switching function which is represented by a linear function havingvariables which comprise a plurality of state quantities of the objectto be controlled (specifically, e.g., a plurality of time series data ofthe difference between the value of the amount-of-heat data and itstarget value). The values of coefficient-parameters of the linearfunction (the coefficients of terms of the linear function) define therate of reduction of the difference. Therefore, the coefficientparameters of the switching function serve as the predeterminedparameter described above.

The above and other objects, features, and advantages of the presentinvention will become apparent from the following description when takenin conjunction with the accompanying drawings which illustrate preferredembodiments of the present invention by way of example.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a control system for controlling aninternal combustion engine according to the present invention;

FIG. 2 is a schematic view of an intake system of the internalcombustion engine controlled by the control system shown in FIG. 1;

FIG. 3 is a diagram illustrative of a basic operation of the controlsystem shown in FIG. 1;

FIG. 4 is a flowchart of a main routine of the control system shown inFIG. 1;

FIG. 5 is a flowchart of the processing sequence of a step in the mainroutine shown in FIG. 4;

FIG. 6 is a diagram illustrative of an operation of the control systemshown in FIG. 1;

FIG. 7 is a diagram illustrative of an operation of the control systemshown in FIG. 1;

FIG. 8 is a diagram illustrative of an operation of the control systemshown in FIG. 1;

FIG. 9 is a diagram illustrative of an operation of the control systemshown in FIG. 1;

FIG. 10 is a diagram illustrative of an operation of the control systemshown in FIG. 1;

FIG. 11 is a diagram illustrative of an operation of the control systemshown in FIG. 1;

FIG. 12 is a diagram illustrative of an operation of the control systemshown in FIG. 1;

FIG. 13 is a diagram illustrative of an operation of the control systemshown in FIG. 1;

FIG. 14 is a flowchart of the processing sequence of a step in the mainroutine shown in FIG. 4;

FIG. 15 is a flowchart of a subroutine in the processing sequence shownin FIG. 14;

FIG. 16 is a flowchart of a subroutine in the subroutine shown in FIG.15;

FIG. 17 is a flowchart of a subroutine in the processing sequence shownin FIG. 15;

FIG. 18 is a flowchart of a subroutine in the processing sequence shownin FIG. 14;

FIG. 19 is a diagram illustrative of an operation of the control systemshown in FIG. 1;

FIG. 20 is a diagram illustrative of an operation of the control systemshown in FIG. 1;

FIG. 21 is a diagram illustrative of an operation of the control systemshown in FIG. 1;

FIG. 22 is a flowchart of the processing sequence of a step in the mainroutine shown in FIG. 4;

FIG. 23 is a flowchart of a subroutine in the processing sequence shownin FIG. 22;

FIG. 24 is a flowchart of a subroutine in the subroutine shown in FIG.23;

FIG. 25 is a diagram illustrative of an operation of the control systemshown in FIG. 1; and

FIG. 26 is a diagram illustrative of a modification of the controlsystem shown in FIG. 1.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

An apparatus for controlling an internal combustion engine according toan embodiment of the present invention will be described below withreference to FIGS. 1 through 25.

FIG. 1 shows in block form a control system for controlling an internalcombustion engine 1 according to the present invention. In FIG. 1, thecontrol system includes a controller 2 for controlling operation of theinternal combustion engine 1.

The internal combustion engine 1 is mounted as a propulsion source on avehicle such as an automobile, a hybrid vehicle or the like (not shown).The internal combustion engine 1 burns a mixture of air and fuel andemits exhaust gases through a catalytic converter 3 comprising athree-way catalyst into the atmosphere.

FIG. 2 schematically shows an intake system of the internal combustionengine 1. As shown in FIG. 2, the internal combustion engine 1 has acombustion chamber 4 which can be supplied with air via a main intakepassage 6 having a throttle valve 5 and a bypass passage 8 connected tothe main intake passage 6 in bypassing relation to the throttle valve 5and having a bypass valve 7. The internal combustion engine 1 also has acylinder 9, a piston 10 reciprocally movable in the cylinder 9, intakeand exhaust valves 11, 12 openably and closably mounted in thecombustion chamber 4, and a chamber 13 in the main intake passage 6.

As shown in FIG. 1, the control system includes, as ancillary componentsfor controlling operation of the internal combustion engine 1, arotational speed sensor 14 for detecting a rotational speed Ne (actualrotational speed) of the internal combustion engine 1, an enginetemperature sensor 15 for detecting an engine temperature Tw (e.g., acoolant temperature), an intake pressure sensor 16 for detecting anintake pressure Pb which is an internal pressure of the main intakepassage 6 downstream of the throttle valve 5 and the bypass valve 7,i.e., an internal pressure of the chamber 13 shown in FIG. 2 in theillustrated embodiment, an atmospheric temperature sensor 17 fordetecting an atmospheric temperature Ta, an atmospheric pressure sensor18 for detecting an atmospheric pressure Pa, an accelerator sensor 19for detecting a manipulated quantity Ap of the accelerator pedal of thevehicle (hereinafter referred to as an “accelerator manipulatedquantity”), and a vehicle speed sensor 20 for detecting a speed V of thevehicle.

The internal combustion engine 1 has, as ancillary components foroperating the internal combustion engine 1, an ignition unit 21 forigniting the air-fuel mixture in the combustion chamber 4, a fuel supplyunit 22 for supplying a fuel into the combustion chamber 4, a throttlevalve actuator 23 for operating the throttle valve 5, and a bypass valveactuator 24 for operating the bypass valve 7.

The vehicle also has a starter motor (not shown) for starting to operatethe internal combustion engine 1, a power supply battery (not shown) forsupplying electric energy to various electric devices on the vehicle,and a transmission, i.e., an automatic transmission in the illustratedembodiment, for transmitting drive power from the ancillary componentsfor controlling operation of the internal combustion engine 1 to drivewheels of the vehicle.

The controller 2, which comprises a microcomputer, controls operation ofthe internal combustion engine 1 with the ignition unit 21, the fuelsupply unit 22, the throttle valve actuator 23, and the bypass valveactuator 24 based on output data (detected values) from the sensors 14through 20, a predetermined program, and preset data values.

The controller 2 has, as functional components, an intake air quantitycontrol means 25 for controlling the quantity of intake air supplied tothe combustion chamber 4 by controlling the opening of the throttlevalve 5 or the bypass valve 7 through the throttle valve actuator 23 orthe bypass valve actuator 24, and an ignition timing control means 26for controlling the ignition timing of the internal combustion engine 1through the ignition unit 21.

Details of the functions of these means 25, 26 will be described lateron. The ignition timing control means 26 has a function as a rotationalspeed control apparatus according to the present invention.

In this embodiment, a control cycle (control period) which is controlledby the controller 2 is a crank angle period (so-called TDC).

Operation of the control system will be described below in combinationwith more specific functions of the intake air quantity control means 25and the ignition timing control means 26.

First, a basic operation of the control system will briefly be describedbelow with reference to FIG. 3. FIG. 3 shows, by way of example,time-dependent changes in the opening of the bypass valve 7 (hereinafterreferred to as a “bypass opening”), the ignition timing, and therotational speed respectively in upper, middle, and lower diagramsections, after the internal combustion engine 1 has started to operateuntil it operates in an idling mode.

In FIG. 3, when the control system is activated by pressing a startswitch (not shown) while the internal combustion engine 1 is not inoperation, the control system first enters an operation mode to startthe internal combustion engine 1 (hereinafter referred to as a “startmode”) by cranking the internal combustion engine 1 with a starter motor(not shown). In the start mode, the bypass opening and the ignitiontiming are controlled as shown, and the rotational speed Ne of theinternal combustion engine 1 varies as shown.

In the control system, the opening of the throttle valve 5 while theinternal combustion engine 1 is in operation is commensurate with theaccelerator manipulated quantity Ap. When the accelerator pedal (notshown) is not depressed (Ap=0, at this time, the internal combustionengine 1 is idling while the vehicle is stopping), the opening of thethrottle valve 5 is nil, i.e., the throttle valve 5 is closed. At thistime, intake air is supplied to the combustion chamber 4 through onlythe bypass passage 8. FIG. 3 shows the operation of the internalcombustion engine 1 when intake air is supplied to the combustionchamber 4 through only the bypass passage S.

When a complete fuel combustion in the internal combustion engine 1 isconfirmed in the start mode, the control system enters an operation mode(hereinafter referred to as a “FIRE mode-) for quickly activating thecatalytic converter 3 while the internal combustion engine 1 is idling.

In the FIRE mode, a command value θCMD for the bypass opening greaterthan in a normal idling mode, i.e., an idling mode other than the FIREmode, is successively generated according to the pattern oftime-dependent changes shown in the upper diagram section of FIG. 3, forexample. The bypass opening is controlled by the bypass valve actuator24 according to the generated command value θCMD for thereby making theamount of intake air introduced into the combustion chamber 4 greaterthan in the normal idling mode.

Basically, the control system operates in the FIRE mode until an elapsedtime t/fire from the start of the FIRE mode (an elapsed time after theamount of intake air has started to increase, hereinafter referred to asa “FIRE elapsed time t/fire”) reaches a predetermined limit timeTFIREIMT (hereinafter referred to as a “FIRE mode limit time TFIRELMT”).

The command value θCMD for the bypass opening in the FIRE mode isbasically established so as to be able to supply exhaust gases having anamount of heat energy sufficient to increase the temperature of andactivate the catalytic converter 3 within the FIRE mode limit timeTFIRELMT (the amount of heat energy of the exhaust gases is essentiallyproportional to the amount of intake air introduced into the internalcombustion chamber 4). Furthermore, the command value θCMD for thebypass opening is established to operate the internal combustion engine1 stably and smoothly in the idling mode while keeping the fuelcombustion and emission of the internal combustion engine 1 in goodconditions in the FIRE mode.

As the amount of intake air increases, i.e., the bypass openingincreases, in the FIRE mode, the rotational speed Ne (actual rotationalspeed) of the internal combustion engine 1 immediately after the amountof intake air has started to increase rises according to the solid-linecurve in the lower diagram section of FIG. 3. When the rotational speedNe reaches a preset rotational speed (NOBJ+NEFSLDS) which is higher thana predetermined idling rotational speed NOBJ (constant) to be finallymaintained as an appropriate rotational speed in the FIRE mode, by agiven value FEFSLDS, the ignition timing of the internal combustionengine 1 is controlled according to the solid-line curve in the middlediagram section of FIG. 3 so as to converge the rotational speed Ne to atarget rotational speed ne/fire according to a feedback control process.This feedback control process will hereinafter be referred to as an“ignition timing control rotational speed F/B control process”. Theignition timing control rotational speed F/B control process is alsostarted when the FIRE elapsed time t/fire reaches a predetermined valueTSLDIGST (see the lower diagram section of FIG. 3), as well as when therotational speed Ne reaches the preset rotational speed (NOBJ+NEFSLDS).

In the ignition timing control rotational speed F/B control process, thetarget rotational speed ne/fire is established according to a patternindicated by the broken line in the lower diagram section of FIG. 3. Thetarget rotational speed ne/fire decreases from the preset rotationalspeed (NOBJ +NEFSLDS) toward the idling rotational speed NOBJ at apredetermined downward gradient. After the target rotational speedne/fire has reached the idling rotational speed NOBJ, the targetrotational speed ne/fire is maintained at the idling rotational speedNOBJ. The idling rotational speed NOBJ is selected to be higher than therotational speed in the normal idling mode.

In the ignition timing control rotational speed F/B control process, acorrective quantity DIG (this corrective quantity DIG is an ignitiontiming difference command value described later on) for the ignitiontiming as indicated by the broken line in the middle diagram section ofFIG. 3 is determined according to a feedback control process so as toconverge the rotational speed Ne (actual rotational speed) of theinternal combustion engine 1 to the target rotational speed ne/fire thusestablished. Then, a basic command value igbase (indicated by thedotand-dash line in the middle diagram section of FIG. 3) for theignition timing is corrected by the corrective quantity DIG to determinea command value iglog for the ignition timing. The basic command valueigbase for the ignition timing corresponds to a command value for theignition timing in a normal operation mode of the internal combustionengine 1 (an operation mode other than the FIRE mode), and represents anadvanced value.

In the ignition timing control rotational speed F/B control process, theignition timing of the internal combustion engine 1 is controlled by theignition unit 21 according to the command value iglog which has beenproduced by correcting the basic command value igbase for therebyconverging the rotational speed Ne of the internal combustion engine 1to the target rotational speed ne/fire (finally to the idling rotationalspeed NOBJ) according to the feedback control process.

At this time, the rotational speed Ne of the internal combustion engine1 tends to be higher than the target rotational speed ne/fire because ofthe increased amount of intake air described above. Therefore, thecorrective quantity DIG determined by the ignition timing controlrotational speed F/B control process corrects the ignition timing so asto be retarded from the basic command value igbase. Consequently, theignition timing iglog produced by correcting the basic command valueigbase with the corrective quantity DIG (≦0) is of a retarded value asindicated by the solid line in the middle diagram section of FIG. 3.

As described above, in the FIRE mode performed when the internalcombustion engine 1 idles initially after it has started to operate, therotational speed Ne of the internal combustion engine 1 is controlled toreach the target rotational speed ne/fire (finally the idling rotationalspeed NOBJ) by increasing the amount of intake air with the controlledbypass opening and retarding the ignition timing according to theignition timing control rotational speed F/B control process, while theamount of heat energy of the exhaust gases emitted from the internalcombustion engine 1 when the air-fuel mixture is burned in thecombustion chamber 4 is made greater than in the normal idling mode.When the exhaust gases with the increased amount of heat energy aresupplied to the catalytic converter 3, the catalytic converter 3 isincreased in temperature and activated quickly, and hence can quicklyprovide a desired exhaust gas purification capability.

The FIRE mode for increasing the amount of intake air and performing theignition timing control rotational speed F/B control process iscontinuously carried out until the FIRE elapsed time t/fire reaches theFIRE mode limit time TFIREIMT, except when the accelerator pedal of thevehicle is depressed while in the FIRE mode. Subsequently, the controlsystem enters the normal operation mode of the internal combustionengine 1. In the normal operation mode, the bypass opening is controlledat an opening (<the bypass opening in the FIRE mode, see a right-handportion of the upper diagram section of FIG. 3) for operating theinternal combustion engine 1 in the normal idling mode, for example.After the end of the FIRE mode, the ignition timing of the internalcombustion engine 1 is gradually returned to a normal advanced ignitiontiming determined by the basic command value igbase, as shows in aright-hand portion of the middle diagram section of FIG. 3.

When the accelerator pedal is depressed to start moving the vehicle orrace the internal combustion engine 1 during the FIRE mode (before theFIRE elapsed time t/fire reaches the FIRE mode limit time TFIRELMT), sothat the internal combustion engine 1 operates in a mode other than theidling mode, the control system interrupts the FIRE mode.

When the control system interrupts the FIRE mode, the amount of intakeair is continuously increased by controlling the bypass opening in orderto reliably increase the temperature of and activate the catalyticconverter 3. However, in order to achieve a desired power outputcapability of the internal combustion engine 1, the ignition timing isreturned to the normal advanced ignition timing determined by the basiccommand value igbase (the ignition timing control rotational speed F/Bcontrol process is interrupted). If the internal combustion engine 1 isto be operated in the idling mode again within the FIRE mode limit timeTFIRELMT, the ignition timing control rotational speed F/B controlprocess is resumed. Therefore, the interruption of the FIRE mode isbasically equivalent to the interruption of the ignition timing controlrotational speed F/B control process. A partial control process forincreasing the amount of intake air by controlling the bypass opening isalso interrupted.

The basic operation of the control system according to the presentembodiment has been described above.

Details of the operation of the control system in view of the basicoperation thereof will be described below.

When the control system is activated while the internal combustionengine 1 is not operating, the controller 2 executes a main routineshown in FIG. 4 in predetermined control cycles, i.e., crank angleperiods (TDC).

First, the controller 2 determines whether the operation mode of thecontrol system is the start mode or not in STEP4-1. specifically, thecontroller 2 determines whether a complete fuel combustion in theinternal combustion engine 1 is confirmed or not. The operation mode ofthe control system is the start mode after the control system isactivated until the complete fuel combustion is confirmed. The completefuel combustion is confirmed on the basis of an output signal from therotational speed sensor 14, i.e., a detected value of the rotationalspeed Ne.

If the operation mode of the control system is the start mode inSTEP4-1, then the controller 2 executes a start mode process forstarting the internal combustion engine 1 in each control cycle inSTEP4-2.

In the start mode process, the controller 2 determines command valuesfor the ignition timing, the amount of fuel to be supplied, and thebypass opening, which are suitable for starting the internal combustionengine 1, based on output signals (detected values) of the sensors 14through 20, predetermined maps, and equations. According to thedetermined command values, the controller 2 operates the ignition unit21, the fuel supply unit 22, and the bypass valve actuator 24 to controlthe ignition timing, the amount of fuel to be supplied, and the bypassopening, while at the same time energizing the starter motor (not shown)to crank the internal combustion engine 1 thereby to start the internalcombustion engine 1.

In the start mode process, the controller 2 initializes variousparameters (described later on) such as flags to be used in a controlprocess of the FIRE mode.

In the start mode process, furthermore, an engine temperature Tw, anatmospheric temperature Ta, and an atmospheric pressure Pa at the timethe internal combustion engine 1 is started are detected respectively bythe engine temperature sensor 15, the atmospheric temperature sensor 17,and the atmospheric pressure sensor 18, and stored in a memory (notshown).

If the operation mode of the control system is not the start mode inSTEP4-1, i.e., if a complete fuel combustion in the internal combustionengine 1 is confirmed, then the controller 2 generates a command valuefor the amount of fuel to be supplied to the internal combustion engine1 in each control cycle in STEP4-3. Then, the controller 2 judgesconditions to determine whether the control process of the FIRE mode isto be carried out or not, i.e., whether the operation mode is to be setto the FIRE mode or the normal mode, in STEP4-4. Thereafter, the intakeair quantity control means 25 generates a command value θCMD for thebypass opening in STEP4-5. The ignition timing control means 26generates a command value iglog for the ignition timing of the internalcombustion engine 1 in STEP4-6.

The controller 2 generates a command value for the amount of fuel to besupplied to the internal combustion engine 1 in STEP4-3 as follows:First, the controller 2 determines a basic amount of fuel to be suppliedbased on a predetermined map from the rotational speed Ne (actualrotational speed) of the internal combustion engine 1 detected by therotational speed sensor 14 and the intake pressure Pb of the internalcombustion engine 1 detected by the intake pressure sensor 16. Thecontroller 2 then corrects the basic amount of fuel to be supplieddepending on the engine temperature Tw and the atmospheric temperatureTa detected respectively by the engine temperature sensor 15 and theatmospheric temperature sensor 17, thereby generating the command valuefor the amount of fuel to be supplied to the internal combustion engine1 in a manner to be commensurate with the amount of intake airintroduced into the combustion chamber 4 of the internal combustionengine 1.

The generated command value for the amount of fuel to be supplied isgiven from the controller 2 to the fuel supply unit 22 in each controlcycle, and the fuel supply unit 22 supplies an amount of fuel to theinternal combustion engine 1 according to the given command value.

In STEP4-4, conditions are judged according to a processing sequenceshown in FIG. 5.

As shown in FIG. 5, the controller 2 determines whether the present FIREelapsed time t/fire is within the FIRE mode limit time TFIRELMT(t/fire<TFIRELMT) or not in STEP5-1, whether the present rotationalspeed Ne detected by the rotational speed sensor 14 is within apredetermined normal range or not in STEP5-2, and whether the enginetemperature Tw detected by the engine temperature sensor 15 is within apredetermined normal range or not in STEP5-3. The FIRE elapsed timet/fire determined in STEP5-1 is initialized to “0” in the start modeprocess in STEP4-2, and starts being measured from the time the startmode is ended (a control cycle in which a complete fuel combustion inthe internal combustion engine 1 is confirmed).

If the conditions in STEPs 5-1 through 5-3 are not satisfied, i.e., ifthe present FIRE elapsed time t/fire has reached the FIRE mode limittime TFIRELMT, the present rotational speed Ne is abnormally high orlow, or the temperature Tw is abnormally high or low, then thecontroller 2 determines whether a learning calculation process, to bedescribed later on, i.e., a process of calculating a basic learningcorrective coefficient vpskisld, to be described later on, is to beended by judging a flag f/flrnend (hereinafter referred to as a“learning calculation end flag f/flrnend”) which is “1” when thelearning calculation process is to be ended and “0” when the learningcalculation process is not to be ended, in STEP5-4. If f/flrnend=0, thenthe controller 2 holds the value of the present FIRE elapsed time t/fireas the value of a parameter t/kil in STEP5-5, and sets the learningcalculation end flag f/flrnend to “1” in STEP5-6. The parameter t/kilserves to represent the FIRE elapsed time t/fire at the time the processof calculating the basic learning corrective coefficient vpskisld isfinished. The parameter t/kil will hereinafter referred to as a“learning end time parameter t/kil”.

The learning calculation end flag f/flrnend and the learning end timeparameter t/kil are initialized to 0” in the start mode process inSTEP4-2.

Then, the controller 2 forcibly fixes the value of the FIRE elapsed timet/fire to the FIRE mode limit time TFIRELMT in STEP5-7, and sets a flagf/fpause, which is “1” when the FIRE mode is to be interrupted and “0”when the FIRE mode is not to be interrupted (hereinafter referred to asa “FIRE interruption flag f/fpause”), and a flag f/fireon, which is “1”when the FIRE mode is to be executed and “0” when the FIRE mode is notto be executed (hereinafter referred to as a “FIRE mode execution on/offflag f/fireon”), to “0” in STEPs 5-8, 5-9. Thereafter, control returnsto the main routine shown in FIG. 4. If the FIRE mode is not to beexecuted (f/fireon=0), then it means that the control system is to beoperated in the normal mode.

If the conditions in STEPs 5-1 through 5-3 are satisfied, then thecontroller 2 determines whether the accelerator pedal of the vehicle isdepressed or not based on an output signal from the accelerator sensor19 (the manipulated quantity Ap of the accelerator pedal) in STEP5-10,and determines whether the internal combustion engine 1 is in a fuelcutting process or not in STEP5-11. The fuel cutting process is aprocess in which the supply of fuel to the internal combustion engine 1is cut off while the vehicle is being decelerated. When the acceleratorpedal of the vehicle is depressed, the controller 2 controls thethrottle valve actuator 23 to adjust the opening of the throttle valve 5to an opening commensurate with the manipulated quantity Ap.

If neither one of the conditions in STEPs 5-10, 5-11 is satisfied, thenthe internal combustion engine 1 is basically to operate in the idlingmode. In this case, the controller 2 sets the FIRE interruption flagf/fpause to SOf in STEP5-12. Then, the controller 2 sets the FIRE modeexecution on/off flag f/fireon to “1” in STEP5-13. Thereafter, controlreturns to the main routine shown in FIG. 4.

If either one of the conditions in STEPs 5-10, 5-11 is satisfied, thenthe controller 2 sets the FIRE interruption flag f/fpause to “1” inorder to interrupt the FIRE mode in STEP5-14, and determines the valueof the learning calculation end flag f/flrnend in STEP5-15. Only iff/flrnend=0, the controller 2 holds the present value of the FIREelapsed time t/fire as the value of the learning end time parametert/kil in STEP5-16, and sets the learning calculation end flag f/flrnendto “1” in STEP5-17.

Then, the controller 2 sets a count-down timer cnt/igvpl used in aprocess of controlling the ignition timing after the interruption of theFIRE mode is finished, to be described later on), to a predeterminedinitial value XCNT in STEP5-18. Thereafter, control executes STEP5-13and returns to the main routine shown in FIG. 4.

The status in which either one of the conditions in STEPs 5-10, 5-11 issatisfied, i.e., the status in which the FIRE interruption flag f/fpauseto “1” in order to interrupt the FIRE mode, is basically a status inwhich the accelerator pedal of the vehicle is depressed to start or runthe vehicle within the FIRE interruption flag f/fpause, i.e., a statusin which the internal combustion engine 1 is actuating it load, or astatus in which the internal combustion engine 1 is racing. However,when the vehicle is started within the FIRE interruption flag f/fpauseand thereafter decelerated, there may be an occasion in which neitherone of the conditions in STEPs 5-10, 5-11 is satisfied. The status inwhich the FIRE mode is interrupted is more accurately a status in whichthe internal combustion engine 1 operates in a mode other than theidling mode while the air-fuel mixture is combusted therein.

In the process of judging conditions in STEP4-4 as described above,after the internal combustion engine 1 has started (after the start modeis finished), insofar as the rotational speed Ne and the enginetemperature Tw are in an appropriate range, the operation mode of thecontrol system is set to the FIRE mode (f/fireon=1) until the FIREelapsed time t/fire reaches the FIRE mode limit time TFIRELMT. In theFIRE mode, the amount of intake air is increased by controlling thebypass opening and the ignition timing control rotational speed F/Bcontrol process is carried out parallel to each other, except when theFIRE mode is interrupted.

If the rotational speed Ne or the engine temperature Tw is abnormallyhigh or low for some reason, the operation mode of the control system isset to the normal mode immediately after the internal combustion engine1 has started or the FIRE mode is canceled (ended) and operation mode isset to the normal mode (f/fireon=0). In the normal mode, the bypassopening and the ignition timing are controlled at values for operatingthe internal combustion engine 1 normally, i.e., in a mode other thanthe FIRE mode. When the operation mode is set to the normal mode, sincethe controller 2 forcibly fixes the value of the FIRE elapsed timet/fire to the FIRE mode limit time TFIRELMT in STEP5-7, the condition inSTEP5-1 will not subsequently be satisfied until the internal combustionengine 1 is started again (the FIRE elapsed time t/fire is initializedonly in the start mode). Therefore, the operation mode is set to theFIRE mode only until the FIRE mode limit time TFIREIMT elapses after theinternal combustion engine 1 has started.

If the vehicle is run by depressing the accelerator pedal or theinternal combustion engine 1 races while the operation mode is being setto the FIRE mode (f/fireon=1), i.e., if the internal combustion engine 1is to operated in a mode other than the idling mode (either one of theconditions in STEPs 5-10, 5-11 is satisfied), then the FIRE interruptionflag f/fpause is set to “1”. In this case, the FIRE mode is interrupted,i.e., whereas the amount of intake air is increased by controlling thebypass opening, the ignition timing control rotational speed F/B controlprocess is performed. If neither one of the conditions in STEPs 5-10,5-11 is satisfied and the FIRE interruption flag f/fpause is reset to“0” while the operation mode is the FIRE mode and interrupted(f/fireon=1 and f/fpause=1) (this is basically a case for resuming theidling mode), then the interruption of the FIRE mode is canceled, andthe ignition timing control rotational speed F/B control process isresumed.

If the FIRE mode is interrupted by depressing the accelerator pedal (thecondition in STEP5-10 is satisfied), then the opening of the throttlevalve 5 is made commensurate with the manipulated quantity Ap of theaccelerator pedal (>0). In this case, therefore, the combustion chamber4 of the internal combustion engine 1 is supplied with intake air viaboth the bypass valve 7 and the throttle valve 5.

Although not employed in the present embodiment, the operation mode ofthe control system may not be set to the FIRE mode until a slight timeelapses after the start mode is ended.

A process of generating a command value θCMD for the bypass opening inSTEP4-5 shown in FIG. 4 will be described below.

Prior to describing specific details of this process, a basic concept ofthe process will first be described below.

In the control system, major processes that the intake air quantitycontrol means 25 carries out for generating a command value θCMD for thebypass opening in the FIRE mode include a process (hereinafter referredto as a “standard opening command value generating process”) ofgenerating a standard command value θ0 for the,bypass opening(hereinafter referred to as a “standard opening command value θ0”), aprocess (hereinafter referred to as a “amount-of-intake-air F/B controlcorrecting process”) of correcting a command value for the bypassopening according to a feedback control process in order to converge anaccumulated value of the actual amount of intake air introduced into thecombustion chamber 4 to a predetermined target value, a process(hereinafter referred to as a “learning correcting process”) of learninga corrective quantity for the command value for the bypass openingaccording to the amount-of-intake-air F/B control correcting processeach time the FIRE mode is performed, and correcting the command valuefor the bypass opening based on the learned corrective quantity, aprocess (hereinafter referred to as an “atmospheric condition correctingprocess”) of correcting the command value for the bypass openingdepending on the atmospheric pressure Pa and the atmospheric temperatureTa detected respectively by the atmospheric pressure sensor 18 and theatmospheric temperature sensor 17, and a process (hereinafter referredto as an “ignition-timing-dependent correcting process”) of correctingthe command value for the bypass opening depending on the ignitiontiming controlled by the ignition timing control rotational speed F/Bcontrol process. Basic concepts of these processes will be describedbelow.

First, the standard opening command value generating process isdescribed below.

In the control system according to the embodiment, the amount of intakeair is increased in the FIRE mode primarily for the purpose of quicklyincreasing the temperature of and activating the catalytic converter 3.It is necessary to increase the amount of intake air so as to be able tosupply the catalytic converter 3 with exhaust gases having an amount ofheat energy (the amount of heat energy of the exhaust gases isessentially proportional to the amount of intake air introduced into thecombustion chamber 4) which is capable of reliably increasing thetemperature of and activating the catalytic converter 3 within the FIREmode limit time TFIRELMT.

The amount of intake air starts to be increased immediately after theinternal combustion engine 1 has started, and while the ignition timingis being controlled so as to be retarded from the normal ignition timingby the ignition timing control rotational speed F/B control process. Ifa pattern of time-dependent changes in the increase of the amount ofintake air is inappropriate, then the combustion and emission statusesof the internal combustion engine 1 may be impaired. Therefore, theamount of intake air needs to be increased in the FIRE mode in order tooperate the internal combustion engine 1 stably and smoothly withoutimpairing combustion and emission statuses of the internal combustionengine 1 in the FIRE mode.

The standard opening command value generating process generates thestandard opening command value θ0, which serves as a basis for thecommand value for the bypass opening to be given to the bypass valveactuator 24 for increasing the amount of intake air, in a feed-forwardmanner in each control cycle (TDC) depending on the engine temperatureTw and the FIRE elapsed time t/fire when the internal combustion engine1 starts (in the start mode).

The standard opening command value generating process is carried out asfollows:

When the internal combustion engine 1 starts (in the start mode), abasic value i/ftbl of the standard opening command value θ0, which is amaximum value of the standard opening command value θ0 while the controlsystem is operating in the FIRE mode, is determined on the basis of apredetermined data table from the engine temperature Tw detected by theengine temperature sensor 15.

In this embodiment, the basic value i/ftbl when the shifted position ofthe shift lever of the automatic transmission (not shown) of the vehicleis in a N (neutral) range in the FIRE mode is different from the basicvalue i/ftbl when the shifted position of the shift lever of theautomatic transmission (not shown) of the vehicle is in a D (drive)range in the FIRE mode.

Specifically, when the shifted position of the automatic transmission isin the N range, a value ifiret (hereinafter referred to as an “N rangebasic value ifiret”) determined according to a data table indicated bythe solid line a in FIG. 6 from the engine temperature Tw at the startof the internal combustion engine 1, is determined as the basic valuei/ftbl of the standard opening command value θ0.

The data table indicated by the solid line a in FIG. 6 is basicallyestablished such that as the engine temperature Tw is higher, the Nrange basic value ifiret is lower. This is because the enginetemperature Tw at the start of the internal combustion engine 1corresponds to the initial temperature of the catalytic converter 3, andas the engine temperature Tw is higher, the amount of heat energyrequired to increase the temperature of and activate the catalyticconverter 3 as desired, i.e., the amount of intake air introduced intothe internal combustion engine 1, may be smaller.

When the shifted position of the automatic transmission is in the Drange, a value which is the sum of a value iatfire (hereinafter referredto as an “D range corrective value iatfire”) determined according to adata table indicated by the solid line b in FIG. 6 from the enginetemperature Tw at the start of the internal combustion engine 1, and theN range basic value ifiret is determined as the basic value i/ftbl(=ifiret+iatfire) of the standard opening command value θ0.

The data table indicated by the solid line b in FIG. 6 is basicallyestablished such that at an arbitrary engine temperature Tw at the startof the internal combustion engine 1, the basic value fitbl in the Drange is set so as to be slightly higher than the N range basic valueifiret. This is because in the D range, a load for absorbing the drivepower of the internal combustion engine 1 is greater than in the Nrange, resulting in a reduction in the rotational speed of the internalcombustion engine 1, and the amount of heat energy of the exhaust gasesis smaller than in the N range.

In the present embodiment, the engine temperature Tw at the start of theinternal combustion engine 1 is used as corresponding to the initialtemperature of the catalytic converter 3, i.e., the temperature of thecatalytic converter 3 at the start of the internal combustion engine 1.When the internal combustion engine 1 starts to operate, the initialtemperature of the catalytic converter 3 may directly be detected, andthe basic value i/ftbl of the standard opening command value θ0 may bedetermined from the detected temperature in the same manner as describedabove.

In this embodiment, since the vehicle has the automatic transmission,the different basic values i/ftbl are used respectively in the N rangeand the D range. If a manual transmission is employed in the vehicle, nosuch different basic values i/ftbl may be used, but a single basic valuei/ftbl may be used depending on the engine temperature Tw at the startof the internal combustion engine 1 or the initial temperature of thecatalytic converter 3 in the same manner as described above.

The basic value i/ftbl of the standard opening command value θ0 isdetermined as described above. In the standard opening command valuegenerating process, furthermore, a corrective coefficient km/fire (≦1)for correcting (by multiplication) the basic value i/ftbl is determinedin each control cycle according to a predetermined data table (timetable) shown in FIG. 7 from the FIRE elapsed time t/fire. A valueproduced when the basic value i/ftbl is multiplied by the correctivecoefficient km/fire is determined as the standard opening command valueθ0 (=i/ftbl·km/fire).

In the data table shown in FIG. 7, during an initial stage (t/fire:0−t1) of the FIRE mode, the corrective coefficient km/fire is graduallyincreased to “1” in order to increase the standard opening command valueθ0 gradually toward the basic value i/ftbl. Then, after the standardopening command value θ0 has reached the basic value i/ftbl (after thecorrective coefficient km/fire has reached “1”), the correctivecoefficient km/fire is set to “1” so as to maintain the standard openingcommand value θ0 at the basic value i/ftbl for a predetermined time(t/fire: t1−t2). Thereafter (t/fire: t2−TFIREIMT), the correctivecoefficient km/fire is gradually reduced in order to gradually reducethe standard opening command value θ0. The standard opening commandvalue θ0 is gradually reduced for the following reason:

When the internal combustion engine 1 is warmed up to a certain extent,the friction of various components of the internal combustion engine 1is gradually reduced, and the rotational speed Ne of the internalcombustion engine 1 tends to increase. As a result, the ignition timingcontrolled by the ignition timing control rotational speed F/B controlprocess becomes more retarded. At this time, when the ignition timing ofthe internal combustion engine 1 reaches a retarded limit value at whichthe ignition timing can be controlled while the internal combustionengine 1 is operating normally, it is no longer possible to suppress theincreasing tendency of the rotational speed Ne of the internalcombustion engine 1. To protect the rotational speed Ne against beingunduly increased, after the FIRE elapsed time t/fire has reached thepreset time t2 and the FIRE mode has proceeded to a certain extent,i.e., after the internal combustion engine 1 has been warmed up to acertain extent, the standard opening command value θ0 (the amount ofintake air introduced into the internal combustion engine 1) isgradually reduced for thereby preventing the rotational speed Ne fromtending to increase due to the reduced friction.

The details of the standard opening command value generating processhave been described above.

In the control system, basically, the bypass opening is controlledaccording to the standard opening command value θ0 that is generated ina feed-forward fashion for thereby operating the internal combustionengine 1 stably and appropriately increasing the temperature of andactivating the catalytic converter 3 as desired.

The amount-of-intake-air FIB control correcting process and theatmospheric condition correcting process will be described below.

The standard opening command value θ0 determined by the standard openingcommand value generating process is determined uniquely in a certainreference correlation of the actual opening of the bypass valve 7 andthe actual amount of intake air introduced into the combustion chamber 4to the command value for the bypass opening given to the bypass valveactuator 24, and is determined under ideal conditions that theatmospheric pressure Pa is a standard atmospheric pressure, e.g., oneatmospheric pressure and the atmospheric temperature Ta is a standardatmospheric pressure, e.g., a normal temperature of 25° C.

The actual opening of the bypass valve 7 or the actual amount of intakeair with respect to the command value for the bypass opening are liableto vary due to variations of the operating characteristics ortimedependent characteristic changes of the bypass valve actuator 24 andthe bypass valve 7 (such variations in the amount of intake air willhereinafter be referred to as “variations due to structural factors”).

Even in the absence of such variations due to structural factors, theactual amount of intake air with respect to the command value for thebypass opening varies depending on the atmospheric pressure Pa. Theactual amount of intake air with respect to the command value θCMD forthe bypass opening also varies depending on the atmospheric temperatureTa though the atmospheric temperature Ta is less influential than theatmospheric pressure Pa such variations in the amount of intake airdepending on the atmospheric pressure Pa and the atmospheric temperatureTa will hereinafter be referred to as “variations due to atmosphericconditions).

Thus, when the command value for the bypass opening is constant (thebypass opening is constant), the actual amount of intake air is smalleras the atmospheric pressure Pa is lower, and since the atmosphericdensity is smaller as the atmospheric temperature Ta is higher, theactual amount of intake air (the mass of intake air) is smaller as theatmospheric temperature Ta is higher.

When the amount of intake air varies, the amount of heat energy (whichis essentially proportional to the amount of intake air) of the exhaustgases emitted by the internal combustion engine 1 also varies, and hencethe pattern of the temperature increase of the catalytic converter 3also varies. In some cases, therefore, the catalytic converter 3 cannotreliably be increased in temperature and activated quickly by increasingthe amount of intake air in the FIRE mode, and the catalytic converter 3cannot have a desired purification capability in the FIRE mode.

The amount-of-intake-air F/B control correcting process and theatmospheric condition correcting process serve to eliminate the abovedrawbacks. The amount-of-intake-air F/B control correcting process is aprocess for compensating for variations due to structural factors, andthe atmospheric condition correcting process is a process forcompensating for variations due to atmospheric conditions.

The amount-of-intake-air F/B control correcting process for compensatingfor variations due to structural factors will first be described below.

The amount-of-intake-air F/B control correcting process has thefollowing basic concept: Amount-of-heat-energy data representing theamount of heat energy actually given to the catalytic converter 3 by theexhaust gases from the internal combustion engine 1 is detected orpredicted successively in each control cycle in the FIRE mode. Thecommand value for the bypass opening is corrected according to afeedback control process in order to converge the value of theamount-of-heat-energy data to a predetermined target value(corresponding to a target amount of heat energy to be applied to thecatalytic converter 3). Based on the corrected command value, the bypassopening is controlled to equalize the actual amount of heat energyapplied to the catalytic converter 3 to a target amount of heat energycorresponding to the target value for the amount-of-heat-energy data. Inthis manner, variations in the pattern of the temperature increase ofthe catalytic converter 3 are eliminated.

The amount-of-heat-energy data representing the amount of heat energyactually given to the catalytic converter 3 may be represented, forexample, by an amount of intake air or an amount of supplied fuel (whichis basically proportional to the amount of heat energy given to thecatalytic converter 3 in each control cycle (at an instantaneous point))in each control cycle (at an instantaneous point), or their integratedvalue (which is proportional to an integrated value of the amount ofheat energy at instantaneous points given to the catalytic converter 3),or an increase in the temperature of the catalytic converter 3 (which isproportional to an integrated value of the amount of heat energy atinstantaneous points given to the catalytic converter 3 by thetemperature increase from the initial temperature of the catalyticconverter 3).

In this embodiment, the integrated value of the amount of intake air isused as the amount-of-heat-energy data. The integrated value of theactual amount of intake air introduced into the internal combustionengine 1 in the FIRE mode is predicted, and a target value for theintegrated value is established in each control cycle as follows:

With respect to the estimation of the integrated value of the amount ofintake air, an amount of intake air introduced into the combustionchamber 1 per TDC or control cycle is substantially proportional to theinternal pressure of the chamber 13, i.e., the intake pressure Pb, asshown in FIG. 2.

In this embodiment, an predicted value gair/pre (hereinafter referred toas an “predicted amount gair/pre of intake air”) for the amount ofintake air per control cycle is determined according to the followingequation (1):

gair/pre=Pb·Gal  (1)

where the coefficient Gal is a predetermined value (constant value).

The predicted amount gair/pre of intake air is accumulated in successivecontrol cycles according to the equation (2) shown below in the FIREmode to determine an integrated value qair/pre of the amount of intakeair (hereinafter referred to as a “predicted integrated amount qair/preof intake air”).

qair/pre(k)=qair/pre(k−1)+gair/pre  (2)

where k represent a control cycle number.

Alternatively, an integrated value of the actual amount of intake airmay be obtained by directly detecting the amount of intake air in eachcontrol cycle with an air flow sensor and integrating the detectedamounts of intake air.

A target value for the integrated value of the amount of intake air(hereinafter referred to as a “target integrated amount qair/cmd ofintake air”), which corresponds to a target value for the integratedvalue of the amount of heat energy given to the catalytic converter 3,can be established in various patterns for appropriately increasing thetemperature of and activating the catalytic converter 3. However, sincethe target value therefor affects the amount of intake air introducedinto the internal combustion engine 1 in the FIRE mode and hence thecombustion and emission statuses of the internal combustion engine 1, itis necessary to take into account the stability of operation of theinternal combustion engine 1.

In the present embodiment, the target integrated amount qair/cmd ofintake air is established on the basis of the standard opening commandvalue θ0 which has been determined to appropriately increase thetemperature of and activate the catalytic converter 3 and operate theinternal combustion engine 1 stably under the ideal conditions.

Specifically, the standard opening command value θ0 has been establishedso as to be able to appropriately increase the temperature of andactivate the catalytic converter 3 and operate the internal combustionengine 1 stably under the ideal conditions that the actual bypassopening and amount of intake air are uniquely determined with respect tothe command value for the bypass opening and the atmospheric pressure Paand the atmospheric temperature Ta are constant standard atmosphericpressure and atmospheric temperature, respectively. Stated otherwise,the standard opening command value θ0 serves to determine an optimumamount of intake air to be drawn into the combustion chamber 4 in orderto appropriately increase the temperature of and activate the catalyticconverter 3 and operate the internal combustion engine 1 stably.

Under the above ideal conditions, the amount of intake air introduced ineach control cycle into the combustion chamber 4 at the time the bypassopening is controlled according to the standard opening command value θ0may be established as a target amount gair/cmd of intake air in eachcontrol cycle, and an accumulated value of the target amount gair/cmd ofintake air may be established as the target integrated amount qair/cmdof intake air.

The target amount gair/cmd of intake air and the target integratedamount qair/cmd of intake air may be determined from the standardopening command value θ0 in each control cycle as follows:

If it is assumed that an actual bypass opening is represented by θ, thenan amount Gi of air passing through the bypass valve 7 per unit time(constant time) is generally expressed, using the atmospheric pressurePa upstream of the bypass valve 7 and the intake pressure Pb downstreamof the bypass valve 7, according to the following equation (3):

Gi=Ci·θ·{square root over (Pa−Pb)}  (3)

where Ci is a coefficient depending on the atmospheric density whichdepends on the atmospheric temperature Ta, and the term of 9 representsthe bypass opening θ0 here though it strictly indicates the effectiveopening area at the bypass valve 7. The coefficient Ci may be selectedto correct any effect which the-bypass opening θ used instead of theeffective opening area has.

When the bypass opening is controlled according to the standard openingcommand value θ0 under the ideal conditions, the bypass opening θbecomes θ=θ0 and the atmospheric pressure Pa becomes Pa=standardatmospheric pressure (constant) in the equation (3), and the coefficientCi is basically a constant value depending on the standard atmosphericpressure. In the steady operating state of the internal combustionengine 1 in the FIRE mode, any variations in the intake pressure Pb arerelatively small, and the intake pressure Pb is generally of a constantvalue. In the steady operating state of the internal combustion engine 1in the FIRE mode, furthermore, the throttle valve 5 is basically closed,and the amount of intake air introduced into the combustion chamber 4can be regarded as being equal to the amount Gi of intake air passingthrough the bypass valve 7.

Thus, the amount of intake air introduced per unit time (constant time)into the combustion chamber 4 when the bypass opening is controlledaccording to the standard opening command value θ0 under the idealconditions is proportional to the standard opening command value θ0.

Accordingly, the amount of intake air introduced per control cycle (TDC)into the combustion chamber 4 when the bypass opening is controlledaccording to the standard opening command value θ0 under the idealconditions, i.e., the target amount gair/cid of intake air, can bedetermined according to the following equation (4): $\begin{matrix}{{{gair}/{cmd}} = {{\theta 0} \cdot \frac{1}{Ne} \cdot {Ga2}}} & (4)\end{matrix}$

The equation (4) includes the term of the reciprocal (1/Ne) of therotational speed Ne of the internal combustion engine 1 because the timeof one control cycle (one TDC) is inversely proportional to therotational speed Ne. A parameter Ga2 in the equation (4) is a constantdetermined according to the standard atmospheric pressure, the standardatmospheric temperature, and the standard intake pressure Pb in thesteady operating state of the internal combustion engine 1 in the FIREmode.

In this embodiment, the target amount gair/cmd of intake air determinedaccording to the equation (4) is accumulated in successive controlcycles according to the equation (5) below while in the FIRE mode,thereby determining the target integrated amount qair/cmd of intake air.

qair/cmd(k)=qair/cmd(k−1)+gair/cmd  (5)

Since the target integrated amount qair/cmd of intake air thusdetermined is determined according to the standard opening command valueθ0, it depends on the engine temperature Tw at the start of the internalcombustion enigine 1 or the initial temperature of the catalyticconverter 3. The amount of intake air to be introduced per control cycleinto the combustion chamber 4 in accordance with the target integratedamount qair/cmd of intake air, i.e., the target amount gair/cmd ofintake air, varies depending on the FIRE elapsed time t/fire in the samepattern of time-dependent changes as the standard opening command valueθ0.

The target integrated amount qair/cmd of intake air may be establishedin advance by a time table, and may be determined from the FIRE elapsedtime t/fire in each control cycle using such a time table.

In the control system, the amount-of-intake-air F/B control correctingprocess is basically performed as follows: A corrective quantity for thecommand value for the bypass opening is determined according to thefeedback control process in order to converge the predicted integratedamount qair/pre of intake air determined as described above (whichcorresponds to the integrated value of the amount of heat energyactually given to the catalytic converter 3) to the target integratedamount qair/cmd of intake air (which corresponds to the target value forthe integrated value of the amount of heat energy to be given to thecatalytic converter 3), i.e., to eliminate any difference between thepredicted integrated amount qair/pre of intake air and the targetintegrated amount qair/cmd of intake air. The standard opening commandvalue θ0 is cor-rected by the corrective quantity thus determined forthereby compensating for variations of the amount of intake air due tostructural factors and hence eliminating variations of the pattern ofthe temperature increase of the catalytic converter 3.

In the amount-of-intake-air F/B control correcting process, it ispreferable to make variable the rate at which the difference between thepredicted integrated amount qair/pre of intake air and the targetintegrated amount qair/cmd of intake air is eliminated, i.e., the rateat which the predicted integrated amount qair/pre of intake air isconverged to the target integrated amount qair/cmd of intake air, underthe existing conditions. For the purpose of making the above ratevariable under the existing conditions, a sliding mode control process,or more specifically an adaptive sliding mode control process, as aresponse designating control-process capable of setting the rate to adesired rate, is employed in the above feedback control process.

In the present embodiment, an algorithm of the amount-of-intake-air F/Bcontrol correcting process for correcting the command value for thebypass opening in order to converge the predicted integrated amountqair/pre of intake air to the target integrated amount qair/cmd ofintake air, using the adaptive sliding mode control process (hereinafterreferred to as an “intake adaptive SLD control process”), is constructedas follows: In the following description, an integrated value of theactual amount of intake air introduced into the combustion chamber 4,including the predicted integrated amount qair/pre of intake air, isreferred to as an integrated amount Qa of intake air, and a target valuefor the integrated amount Qa of intake air is referred to as a targetintegrated amount q (corresponding to the target integrated amountqair/cmd of intake air). The command value for the bypass opening isgenerally referred to as an opening command Θ.

The actual amount of intake air introduced into the combustion chamber 4in each control cycle is represented by Gcyl, and the correlationbetween the amount Gcyl of intake air and the opening command Θ isexpressed by a discrete-system (discrete-time system) model (primaryautoregressive model) of a time lag of first order, as indicated by thefollowing equation (6):

Gcyl(k+1)=α·Gcyl(k)+β·Θ(k)  (6)

where α, β are model parameters depending on the atmospheric pressurePa, the atmospheric temperature Ta, the intake pressure Pb, and therotational speed Ne, etc.

Since the integrated amount Qa of intake air in each control cycle isrepresented by the following equation (7):

Qa(k)=Qa(k−1)+Gcyl(k)  (7)

The following equation (8) is derived from the equations (7) and (6):$\begin{matrix}\begin{matrix}{{{Qa}( {k + 1} )} = {{{Qa}(k)} + {{Gcyl}( {k + 1} )}}} \\{= {{{Qa}(k)} + {\alpha \cdot {Gcyl}} + {\beta \cdot {\Theta (k)}}}}\end{matrix} & (8)\end{matrix}$

Because Gcyl(k) is Gcyl(k)=Qa(k)−Qa(k−1) according to the equation (7),Gcyl(k)=Qa(k)−Qa(k−1) is put in the equation (8) and the equation (8) ismodified into the following equation (9):

$\begin{matrix}{\begin{matrix}{{{Qa}( {k + 1} )} = {{{Qa}(k)} + {\alpha \cdot ( {{{Qa}(k)} - {{Qa}( {k - 1} )}} )} + {\beta \cdot {\Theta (k)}}}} \\{= {{( {1 + \alpha} ) \cdot {{Qa}(k)}} - {\alpha \cdot ( {{{Qa}( {k - 1} )} + {\beta \cdot {\Theta (k)}}} }}}\end{matrix}\begin{matrix}{{\therefore{{Qa}( {k + 1} )}} = {{{a1} \cdot {{Qa}(k)}} + {{b1} \cdot {{Qa}( {k - 1} )}} + {{C1} \cdot {\Theta (k)}}}} \\( {{{a1} = {1 + \alpha}},{{b1} = {- \alpha}},{{C1} = \beta}} )\end{matrix}} & (9)\end{matrix}$

The equation (9) expresses a system for generating the integrated amountQa of intake air from the opening command Θ, i.e., a system to becontrolled by the intake adaptive SLD control process, in terms of adiscrete-system model (secondary autoregressive model, hereinafterreferred to as an “intake-side controlled model”). The intake-sidecontrolled model expresses the integrated amount Qa(k+1) of intake airin each control cycle as the output of the system to be controlled bythe intake adaptive SLD control process, using time-series data Qa(k),Qa(k−1) of the integrated amount Qa of intake air in past control cyclesand the opening command Θ(k) as the input of the system to be controlledby the intake adaptive SLD control process. In the equation (9),coefficients a1, a2 relative to the integrated amounts Qa(k), Qa(k−1) ofintake air and a coefficient b1 relative to the opening command Θ(k) aremodel parameters defining the behavioral characteristics of theintake-side controlled model.

According to the present embodiment, an algorithm of the intake adaptiveSLD control process is constructed, based on the intake-side controlledmodel, as follows:

In the intake adaptive SLD control process, a switching function alrequired for the sliding mode control process is defined by a linearfunction according the equation (10), shown below, where time-seriesdata Eq(k), Eq(k−1) in each control cycle of the difference Eq=Qa−qbetween the integrated amount Qa of intake air and the target integratedamount q are variables. $\begin{matrix}\begin{matrix}{{{\sigma 1}(k)} = {{{s1} \cdot ( {{{Qa}(k)} - {q(k)}} )} + {{s2} \cdot ( {{{Qa}( {k - 1} )} - {q( {k - 1} )}} )}}} \\{= {{{s1} \cdot {{Eq}(k)}} + {{s2} \cdot {{Eq}( {k - 1} )}}}}\end{matrix} & (10)\end{matrix}$

where s1, s2 are coefficient parameters of the terms of the switchingfunction σ1. These coefficient parameters s1, s2 are selected to satisfythe condition of the following inequality (11): $\begin{matrix}{{{- 1} < \frac{s2}{s1} < 1}( {{{{when}\quad {s1}} = 1},{{- 1} < {s2} < 1}} )} & (11)\end{matrix}$

In this embodiment, the coefficient parameter s1 is set to s1=1 for thesake of brevity. Furthermore, the value of the coefficient parameter s2(more generally, the value of s2/s1) is variably selected, as describedlater on.

With the switching function al thus defined, if state quantities (Eq(k),Eq(k−1)) comprising the set of the time-series data Eq(k), Eq(k−1) ofthe difference Eq=Qa−q are converged onto a switching curve (alsoreferred to as a sliding curve) defined by σ1=0 as shown in FIG. 8 andremain converged, then the state quantities (Eq(k), Eq(k−1)) can beconverged to a balanced point on the switching curve σ1=0, i.e., a pointwhere Eq(k)=Eq(k−1)=0, highly stably without being affected bydisturbances.

In the present embodiment, the phase space relative to the switchingfunction σ1 is two-dimensional (the state quantities (Eq(k), Eq(k−1))have two components), so that the switching curve σ1=0 is represented bya straight line. If the phase space is three-dimensional, then theswitching curve becomes a plane and may be referred to as a slidingplane. If the phase space is four-dimensional or n-dimensional where nis greater than four, then the switching curve is a hyperplane thatcannot be geometrically illustrated.

A control input generated by the intake adaptive SLD control process asan input to be given to the controlled model according to the equation(9), i.e., the opening command Θ, for converging the integrated amountQa of intake air to the target integrated amount q is basically the sumof an equivalent control input Θeq determined according to a control lawfor converging the state quantities (Eq(k), Eq(k−1)) onto the switchingcurve σ1=0, a reaching law input Θrch determined according to a reachinglaw which is-a control law for converging the state quantities (Eq(k),Eq(k−1)) onto the switching curve σ1=0, and an adaptive law input Θadpdetermined according to an adaptive law (adaptive algorithm) which is acontrol law for eliminating the effect of disturbances or the like whenthe state quantities (Eq(k), Eq(k−1)) are converged onto the switchingcurve σ1=0 (see the following equation (12)).

Θ=Θeq+Θrch+Θadp  (12)

In a normal sliding mode control process, the adaptive law is notconsidered, and the adaptive law input Θadp is omitted.

The equivalent control input Θeq is given by the following equation(13): $\begin{matrix}\begin{matrix}{{\Theta \quad {{eq}(k)}} = \quad {\frac{- 1}{{s1} \cdot {b1}} \cdot \lbrack {{( {{{s1} \cdot ( {{a1} - 1} )} + {s2}} ) \cdot {{Qa}(k)}} +} }} \\{\quad {{( {{{s1} \cdot {a2}} - {s2}} ) \cdot {{Qa}( {k - 1} )}} -}} \\{\quad {{{s1} \cdot ( {{q( {k + 1} )} - {q(k)}} )} -}} \\{\quad  {{s2} \cdot ( {{q(k)} - {q( {k - 1} )}} )} \rbrack}\end{matrix} & (13)\end{matrix}$

The equation (13) can be derived on the basis of the conditionσ1(k)=σ1(k−1) for converging the state quantities (Eq(k), Eq(k−1)) ontothe switching curve σ1=0 and the equation (9) of the intake-sidecontrolled model.

Various schemes are considered for determining the reaching law inputΘrch and the adaptive law input Θadp. In this embodiment, the reachinglaw input Θrch and the adaptive law input Θadp are made proportional tothe value of the switching function σ1 and the integrated value(integral) of the value of the switching function σ1, and are determinedby the following respective equations (14), (15) $\begin{matrix}{{\Theta \quad {{rch}(k)}} = {\frac{- 1}{{s1} \cdot {b1}} \cdot {F1} \cdot {{\sigma 1}(k)}}} & (14) \\{{\Theta \quad {{adp}(k)}} = {\frac{- 1}{{s1} \cdot {b1}} \cdot {F2} \cdot {\sum\limits_{i = 0}^{k}{{\sigma 1}(i)}}}} & (15)\end{matrix}$

F1 in the equation (14) is a coefficient for defining a gain relative tothe reaching law, and may be established to satisfy the inequality (16)shown below. For reducing chattering upon converging the value of theswitching function σ1 onto the switching curve σ1=0. the coefficient F1should preferably be established to satisfy the following inequality(16)′:

0<F1<2  (16)

0<F1<1  (16)′

F2 in the equation (15) is a coefficient for defining a gain relative tothe adaptive law, and may be established to satisfy the equation (17)shown below. ΔT in the equation (17) represent a control cycle (controlperiod). $\begin{matrix}{{{F2} = {J \cdot \frac{2 - {F1}}{\Delta \quad T}}}( {0 < J < 2} )} & (17)\end{matrix}$

According to the algorithm of the intake adaptive SLD control processemployed in the present embodiment, it is possible to control the amountof intake air in the FIRE mode for converging the integrated amount Qaof intake air to the target integrated amount q by determining theequivalent control input Θeq, the reaching law input Θrch, and theadaptive law input Θadp, and generating their sum as the opening commandΘ according to the equations (13) through (15).

In order to determine the equivalent control input Θeq, the reaching lawinput Θrch, and the adaptive law input Θadp according to the equations(13) through (15), it is necessary to identify values of the modelparameters a1, a2, b1 of the intake controlled model expressed by theequation (9). However, since the values of these model parameters a1,a2, b1 tend to be affected by various factors in the FIRE mode, it isliable to be complex to optimally identify their values.

According to the present embodiment, there is constructed a simplifiedalgorithm of the intake adaptive SLD control process, from which themodel parameters a1, a2, b1 have been eliminated, as follows:

With respect to the reaching law input Θrch and the adaptive law inputΘadp, only the model parameter included in the equations (14), (15) fordetermining the reaching law input Θrch and the adaptive law input Θadpis b1. Replacing (F1/b1) with Fx in the equation (14) and replacing(F2/b1) with Fy in the equation (15), the equations (14), (15) can bemodified into the following equations (18), (19): $\begin{matrix}{{\Theta \quad {{rch}(k)}} = {\frac{- 1}{s1} \cdot {Fx} \cdot {{\sigma 1}(k)}}} & (18) \\{{\Theta \quad {{adp}(k)}} = {\frac{- 1}{s1} \cdot {Fy} \cdot {\sum\limits_{i = 0}^{k}{{\sigma 1}(i)}}}} & (19)\end{matrix}$

Therefore, the reaching law input Θrch and the adaptive law input Θadpcan be determined, without using the model parameter b1, according tothe equations (18), (19).

The coefficients Fx, Fy in, the equations (18), (19) may be determinedby experimentation and simulation in view of the stability and quickresponse of the convergence of the value of the switching function σ1onto the switching curve σ1=0.

With respect to the equivalent control input Θeq, the equation (13) fordetermining the equivalent control input Θeq can be modified into thefollowing equation (20), using the difference Eq=Qa−q: $\begin{matrix}\begin{matrix}{{\Theta \quad {{eq}(k)}} = \quad {\frac{- 1}{{s1} \cdot {b1}}\lbrack {{( {{{s1} \cdot ( {{a1} - 1} )} + {s2}} ) \cdot {{Eq}(k)}} +} }} \\{{\quad  {( {{{s1} \cdot {a2}} - {s2}} ) \cdot {{Eq}( {k - 1} )}} \rbrack} +} \\{\quad {\frac{- 1}{b1} \cdot \lbrack {{- {q( {k + 1} )}} + {{a1} \cdot {q(k)}} + {{a2} \cdot {q( {k - 1} )}}} \rbrack}}\end{matrix} & (20)\end{matrix}$

In the equation (20), the term including the first brackets is afeedback term based on the difference Eq between the integrated amountQa of intake air and the target integrated amount q, and the termincluding the second brackets is a feed-forward term based on only thetarget integrated amount q. The feedback term and the feed-forward termare represented respectively by Θeq/fb, Θeq/ff and expressed accordingto the following equations (21), (22): $\begin{matrix}\begin{matrix}{{\Theta \quad {{eq}/{fb}}} = \quad {\frac{- 1}{{s1} \cdot {b1}}\lbrack {{{( {{{s1} \cdot ( {{a1} - 1} )} + {s2}} ) \cdot {Eq}}(k)} +} }} \\{\quad  {( {{{s1} \cdot {a2}} - {s2}} ) \cdot {{Eq}( {k - 1} )}} \rbrack}\end{matrix} & (21) \\{{\Theta \quad {{eq}/{ff}}} = {\frac{- 1}{b1}\lbrack {{- {q( {k + 1} )}} + {{a1} \cdot {q(k)}} + {{a2} \cdot {q( {k - 1} )}}} \rbrack}} & (22)\end{matrix}$

The feed-forward term Θeq/ff is an input (opening command Θ) to be givento the controlled model in such a state that the difference Eq issteadily “0”. The standard opening command value θ0 serves to determinethe target integrated amount q in this embodiment, and is established ina feed-forward manner such that the amount of intake air and hence theintegrated amount of intake air will uniquely be determined to be atarget value thereof with respect to the standard opening command valueθ0.

Therefore, the feed-forward term Θeq/ff in the equation (20) can bereplaced with the standard opening command value θ0 which does notinclude the model parameters a1, a2, b1.

The equivalent control input Θeq including the feedback term Θeq/fb is acontrol input for converging the state quantities (Eq(k), Eq(k−1)) ontothe switching curve σ1=0. According to studies conducted by theinventors of the present invention, the equivalent control input Θeq ishighly stable in such a state that the state quantities (Eq(k), Eq(k−1))are present in the vicinity of the switching curve σ1=0, in the controlsystem according to the present embodiment. In the present embodiment,furthermore, the stability of the convergence of the state quantities(Eq(k), Eq(k−1)) onto the switching curve σ1=0 can be increased by usingthe adaptive law input Θadp.

In control system according to the present embodiment, therefore, it isconsidered that controllability will not practically be impaired even ifthe feedback term Θeq/fb is omitted.

In view of the above analysis, the equivalent control input Θeq may bemodified by omitting the feedback term Θeq/fb thereof and replacing thefeed-forward term Θeq/ff with the standard opening command value θ0. Theequivalent control input Θeq thus modified can be determined withoutusing the model parameters a1, a2, b1.

In this embodiment, the equivalent control input Θeq in the intakeadaptive SLD control process is expressed by the following equation(23):

Θeq=θ0  (23)

In the amount-of-intake-air F/B control correcting process, an input tobe given to the controlled model determined in the intake adaptive SLDcontrol process in order to compensate for variations in the amount ofintake air due to structural factors, i.e., the opening command Θ, isdetermined according to the following equation (24): $\begin{matrix}\begin{matrix}{{\Theta (k)} = {{{\theta 0}(k)} + {\Theta \quad {{rch}(k)}} + {\Theta \quad {{adp}(k)}}}} \\{= {{\theta \quad 0(k)} + {\frac{- 1}{s1}\lbrack {{{Fx} \cdot {{\sigma 1}(k)}} + {{Fy} \cdot {\sum\limits_{i = 0}^{k}{{\sigma 1}(i)}}}} \rbrack}}}\end{matrix} & (24)\end{matrix}$

Stated otherwise, the sum (=Θrch+Θadp) of the reaching law input Θrchand the adaptive law input Θadp determined according to the equations(18), (19) is determined as a corrective quantity i/sld for the commandvalue for the bypass opening (hereinafter referred to as an “SLD openingcorrective quantity i/sld”) according to the equation (25) shown below.By then correcting the standard opening command value θ0 with the SLDopening corrective quantity i/sld, i.e., adding the SLD openingcorrective quantity i/sld to the standard opening command value θ0, theopening command Θ for compensating for variations in the amount ofintake air due to structural factors is determined. $\begin{matrix}\begin{matrix}{{i/{{sld}(k)}} = {{\Theta \quad {{rch}(k)}} + {\Theta \quad {{adp}(k)}}}} \\{= {\frac{- 1}{s1}\lbrack {{{Fx} \cdot {{\sigma 1}(k)}} + {{Fy} \cdot {\sum\limits_{i = 0}^{k}{{\sigma 1}(i)}}}} \rbrack}}\end{matrix} & (25)\end{matrix}$

The value of the switching function σ1 required to determine the SLDopening corrective quantity i/sld (=Θrch+Θadp) is determined accordingto the following equation (26) which employs the predicted integratedamount qair/pre of intake air determined according to the equation (2)as the integrated amount Qa of intake air according to the equation (10)and which employs the target integrated amount qair/cmd of intake airdetermined according to the equation (5) as the target integrated amountq: $\begin{matrix}\begin{matrix}{{{\sigma 1}(k)} = \quad {{{s1} \cdot {{Eq}(k)}} + {{s2} \cdot {{Eq}( {k - 1} )}}}} \\{= \quad {{{s1} \cdot ( {{{qair}/{{pre}(k)}} - {{qair}/{{cmd}(k)}}} )} +}} \\{\quad {{s2} \cdot ( {{{qair}/{{pre}( {k - 1} )}} - {{qair}/{{cmd}( {k - 1} )}}} )}}\end{matrix} & (26)\end{matrix}$

In this embodiment, while the FIRE mode is being interrupted with theFIRE interruption flag f/fpause being set to “1”, the calculation of theSLD opening corrective quantity i/sld is interrupted, i.e., the SLDopening corrective quantity i/sld is kept at its value immediately priorto the interruption of the FIRE mode. However, the calculation of thepredicted integrated amount qair/pre of intake air and the targetintegrated amount qair/cmd of intake air is continued (the calculationof the predicted integrated amount qair/pre of intake air is not whilethe internal combustion engine 1 is in the fuel cutting process). If theinterruption of the FIRE mode is canceled prior to the elapse of theFIRE mode limit time TFIRELMT, then the calculation of the SLD openingcorrective quantity i/sld and the correction of the standard openingcommand value θ0 depending thereon are resumed.

The foregoing process is performed for the following reasons: While theFIRE mode is being interrupted, the vehicle is propelled or the internalcombustion engine 1 is raced by depressing the accelerator pedal. Inthis condition, since the throttle valve 5 is opened to an openingdepending on the accelerator manipulated quantity Ap, the actual amountof intake air introduced into the combustion chamber 4 is the sum of theamount of intake air passing through the bypass valve 7 and the amountof intake air passing through the throttle valve 5.

In this condition, the predicted integrated amount qair/pre of intakeair is equal to an integrated value of the amount of intake air passingthrough both the bypass valve 7 and the throttle valve 5. It is notpreferable to control the bypass opening in order to converge thepredicted integrated amount qair/pre of intake air to the targetintegrated amount-qair/cmd of intake air determined depending on thestandard opening command value θ0 for the bypass valve 7, for thepurpose of achieving a desired power output capability of the internalcombustion engine 1 depending on the depression of the acceleratorpedal. In this embodiment, therefore, the calculation of the SLD openingcorrective quantity i/sld is interrupted while the FIRE mode is beinginterrupted.

Moreover, while the FIRE mode is being interrupted, since the actualamount of intake air introduced into the combustion chamber 4 is equalto the sum of the amount of intake air passing through the bypass valve7 and the amount of intake air passing through the throttle valve 5, theamount of heat energy applied to the catalytic converter 3 is furtherincreased. Though the catalytic converter 3 may be sufficientlyincreased in temperature and activated while the FIRE mode is beinginterrupted, the interruption of the FIRE mode may often be canceled,and the catalytic converter 3 may not be sufficiently increased intemperature and activated when the interruption of the FIRE mode iscanceled. In this embodiment, therefore, while the FIRE mode is beinginterrupted, the calculation of the predicted integrated amount qair/preof intake air and the target integrated amount qair/cmd of intake air iscontinued, and after the interruption of the FIRE mode is canceled, thecalculation of the SLD opening corrective quantity i/sld is resumed tocorrect the standard opening command value θ0. In this manner, thecatalytic converter 3 is reliably increased in temperature and activatedduring -the interruption of the FIRE mode. However, since the air drawninto the combustion chamber 4 does not contribute to the heat energygiven to the catalytic converter 3 while the internal combustion engine1 is in the fuel cutting process, the calculation of the predictedintegrated amount qair/pre of intake air is not calculated while theinternal combustion engine 1 is in the fuel cutting process.

The calculation of the SLD opening corrective quantity i/sld isinterrupted, i.e., the SLD opening corrective quantity i/sld is kept atits value immediately prior to the interruption of the FIRE mode, evenwhen the ignition-timing-dependent correcting process, described lateron, is performed. The reason for this is as follows: Theignition-timing-dependent correcting process, whose details will bedescribed later on, is a process of correcting the opening command Θ soas to be reduced in a feed-forward manner with respect to the standardopening command value θ0. If the SLD opening corrective quantity i/sldis calculated when the ignition-timing-dependent correcting process iscarried out, then the SLD opening corrective quantity i/sld iscalculated in a manner to cancel the reduction in the opening command Θcorrected by the ignition-timing-dependent correcting process.

The basic concept of the amount-of-intake-air F/B control correctingprocess has been described above.

A stage immediately after the amount of intake air introduced into theinternal combustion engine 1 starts being increased, i.e., a stage inwhich the bypass opening is increased, is immediately after the internalcombustion engine 1 starts operating. If the standard opening commandvalue θ0 is corrected largely by the SLD opening corrective quantityi/sld in this stage, then the combustion and emission statuses in thecombustion chamber 4 of the internal combustion engine 1 may beimpaired. In this embodiment, furthermore, since the target integratedamount qair/cmd of intake air is premised on a steady intake state ofthe internal combustion engine 1, the reliability of the targetintegrated amount qair/cmd of intake air is considered to be poor in thestage immediately after the amount of intake air introduced into theinternal combustion engine 1 starts being increased. Therefore, in thestage immediately after the amount of intake air introduced into theinternal combustion engine 1 starts being increased, the difference Eqbetween the target integrated amount qair/cmd of intake air and thepredicted integrated amount qair/pre of intake air tends to be large,and hence the SLD opening corrective quantity i/sld also tends to belarge.

In view of the above considerations, according to theamount-of-intake-air F/B control correcting process, the values of thetarget integrated amount qair/cmd of intake air and the predictedintegrated amount qair/pre of intake air are forcibly set to “0” (Eq=0)until a predetermined time TISLDLMT (hereinafter referred to as an USLDcorrection limit time TISLDLMT”, see FIG. 7) elapses, i.e., until theFIRE elapsed time t/fire≧TISLDLMT, after the amount of intake airintroduced into the internal combustion engine 1 starts being increased,i.e., after the FIRE mode starts being carried out. With such a setting,the value of the SLD opening corrective quantity i/sld is kept as “0”,and hence the standard opening command value θ0 is not corrected by theSLD opening corrective quantity i/sld, immediately after the internalcombustion engine 1 starts to operate until the FIRE elapsed time t/firereaches the SLD correction limit time TISLDLMT.

In the amount-of-intake-air F/B control correcting process, immediatelyafter the standard opening command value θ0 starts being actuallycorrected by the SLD opening corrective quantity i/sld, if the standardopening command value θ0 is corrected abruptly, then the combustionstatus and emission capability of the internal combustion engine 1 maybe impaired. In this embodiment, therefore, based on the responsedesignating characteristics of the intake adaptive SLD control processused in the amount-of-intake-air F/B control correcting process, therate of reduction of the difference Eq (hereinafter referred to as an“intake difference Eq”) between the target integrated amount qair/cmd ofintake air and the predicted integrated amount qair/pre of intake air,i.e., the rate at which the predicted integrated amount qair/pre ofintake air is converged to the target integrated amount qair/cmd ofintake air, is variably established as described below.

In the intake adaptive SLD control process, the state quantities (Eq(k),Eq(k−1)) relative to the intake difference Eq are converged onto theswitching curve σ1=0, the following equation (27) is satisfied as isapparent from the equation (10): $\begin{matrix}{{{Eq}(k)} = {{{- \frac{s2}{s1}} \cdot {{Eq}( {k - 1} )}} = {{{- {pole}}/i} \cdot {{Eq}( {k - 1} )}}}} & (27)\end{matrix}$

Therefore, the value of the ratio (s2/s1) (−1<s2/s1<1) of thecoefficient parameters s1, s2 of the switching function σ1 determinesthe rate of reduction of the intake difference Eq to “0” (as the |s2/s1|approaches “0”, the rate of reduction increases). Consequently, it ispossible to designate the rate of reduction of the intake difference Eqwith the value of the ratio (s2/s1). This is referred to as the responsedesignating characteristics of the intake adaptive SLD control process.

Increasing the rate of reduction of the intake difference Eq isequivalent to increasing the gain of the feedback control according tothe intake adaptive SLD control process. The equation (27) expresses asystem of a time lag of first order without inputs, and the ratio(s2/s1) corresponds to a pole of the system of a time lag of first order(the ratio (s2/s1) will hereinafter be referred to as a “pole pole/in”).In this embodiment, the coefficient parameter s1 is set to s1=1, withpole/i=s2. The reduction of the intake difference Eq to “0” ispreferably aperiodic. In this embodiment, therefore, s2/s1=pole/i<0 (ifs2/s1>0, then the reduction of the intake difference Eq to “0” isoscillatory as can be seen from the equation (27)).

In the amount-of-intake-air F/B control correcting process, based on theresponse designating characteristics of the intake adaptive SLD controlprocess, a value pole/itbl (hereinafter referred to as a “pole tablevalue pole/itbl”) determined in each control cycle from the FIRE elapsedtime t/fire based on a predetermined data table (time table) shown inFIG. 9 is basically established as the value of the pole pole/i. In thismanner, the value of the pole pole/i is established variably dependingon the FIRE elapsed time t/fire.

In the data table shown in FIG. 9, after the FIRE elapsed time t/firereaches a predetermined value TPOLEVST (TPOLEVST≧SLD correction limittime TISLDLMT), as the FIRE elapsed time t/fire increases, the poletable value pole/itbl and the pole pole/i are gradually increased from apredetermined lower limit value pole/i0 (<0, “−1” in the embodiment) toa predetermined steady value pole/ix (pole/i0<pole/ix<0), i.e., theabsolute value of the pole table value pole/itbl is gradually reduced.After the pole table value pole/itbl has reached the steady valuepole/ix, i.e., after the FIRE elapsed time t/fire has reached apredetermined value TPOLEX shown in FIG. 9, the pole table valuepole/itbl maintained at the steady value pole/ix. Consequently,immediately after the standard opening command value θ0 starts to becorrected by the SLD opening corrective quantity i/sld, the rate ofreduction of the intake difference Eq is gradually increased, i.e., thepredicted integrated amount qair/pre of intake air is slowly convergedto the target integrated amount qair/cmd of intake air, and until theFIRE elapsed time t/fire reaches the predetermined value TPOLEX, therate of reduction of the intake difference Eq is made lower than afterthe FIRE elapsed time t/fire reaches the predetermined value TPOLEX.

The pole pole/i is increased by the pole table value pole/itbl asdescribed above basically in an initial stage after the internalcombustion engine 1 starts to operate, i.e., a stage in which the amountof intake air increases.

According to the present embodiment, while the FIRE mode is beinginterrupted, the amount-of-intake-air F/B control correcting process, ormore accurately the process of calculating the SLD opening correctivequantity i/sld, is not carried out. In this condition, the pole pole/iis set to the lower limit value pole/i0 of the pole table valuepole/itbl. When the interruption of the FIRE mode is canceled, the polepole/i is gradually returned from the lower limit value pole/i0 to thepole table value pole/itbl (see the imaginary-line curve in FIG. 9).

The atmospheric condition correcting process for compensating forvariations in the amount of intake air due to atmospheric conditionswill be described below.

The atmospheric pressure of the atmospheric conditions will first bedescribed below. It is assumed that the atmospheric temperature isconstant and the bypass opening is equal to the opening command Θ.

If it is assumed that the pressure in the combustion chamber 4 of theinternal combustion engine 1 is represented by Pcyl and the opening(effective opening area) of the intake valve 11 (see FIG. 2) by Acyl,then the amount Gcyl of intake air introduced into the combustionchamber 4 is expressed by the following equation (28), using thepressure Pcyl, the opening Acyl, and the intake pressure Pb:

Gcyl=Ci·Acyl·{square root over (Pb−Pcyl)}  (28)

where Ci is a coefficient depending on the atmospheric density asdescribed above with respect to the equation (3).

In the internal combustion engine 1, the pressure Pcyl in the combustionchamber 4 and the opening Acyl of the intake valve 11 are basicallyconstant. The coefficient Ci may be considered to be constant if theatmospheric temperature Ta is constant.

It can be seen from the equation (28) that in order to make the amountGcyl of intake air in the combustion chamber 4 independent of theatmospheric pressure, it is necessary that the intake pressure Pb do notchange depending on the atmospheric pressure Pa.

The amount Gi of air passing through the bypass valve 7 depending on theopening command Θ for the bypass opening is expressed by the followingequation (29), as with the equation (3):

Gi=Ci·Θ·{square root over (Pa−Pb)}  (29)

When the atmospheric pressure Pa is a standard atmospheric pressure(hereinafter referred to as a standard atmospheric pressure Pa“0”), theamount Gi0 of air (hereinafter referred to as a “standard amount Gi0 ofair”, which corresponds to the target amount gair/cmd of intake air)passing through the bypass valve 7 at the time the opening command Θ isset to the standard opening command value θ0 (which is determined on thebasis of the standard atmospheric pressure Pa0) is expressed by thefollowing equation (30):

Gi0=Ci·θ0·{square root over (Pa0+L −Pb0+L )}  (30)

where Pb0 represents an intake pressure (hereinafter referred to as a“standard intake pressure Pb0”) generated in the chamber 13 (see FIG. 2)when the bypass opening is equalized to the standard opening commandvalue θ0 under the standard atmospheric pressure Pa0.

According to the known characteristic equation of gases, the conditionfor the intake pressure Pb in the chamber 13 not to vary is that theamount of air flowing into the chamber 13, i.e., the amount Gi of airpassing through the bypass valve 7, be equal to the amount of airflowing out of the chamber 13, i.e., the amount Gcyl of intake airintroduced into the combustion chamber 4.

From the foregoing, the opening command Θ for keeping the amount Gcyl ofintake air introduced into the combustion chamber 4 unchanged when theatmospheric pressure Pa varies with respect to the standard atmosphericpressure Pa0 may be determined such that the intake pressure Pb in theequation (29) is equalized to the standard intake pressure Pb0 and theamount Gi of air expressed by the equation (29) is equalized to thestandard amount Gi0 (equation 30) of air.

That is, the opening command Θ may be determined to satisfy thefollowing equation (31):

Ci·Θ·{square root over (Pa−Pb0+L )}=Ci·θ0·{square root over (Pa0+L−Pb0+L )}  (31)

When solving the equation (31) for the opening command Θ, the followingequation (32) is obtained: $\begin{matrix}{\begin{matrix}{\Theta = {{\theta 0} \cdot \sqrt{\frac{{Pa0} - {Pb0}}{{Pa} - {Pb0}}}}} \\{= {{\theta 0} \cdot {kpa}}}\end{matrix}( {{kpa} = \sqrt{\frac{{Pa0} - {Pb0}}{{Pa} - {Pb0}}}} )} & (32)\end{matrix}$

Basically, therefore, it is possible to compensate for variations in theamount of intake air depending on the atmospheric pressure by correctingthe standard opening command value θ0 to determine the opening command ebased on the equation (32). Specifically, an opening command tocompensate for variations in the amount of intake air depending on theatmospheric pressure can be determined by multiplying the openingcommand by the value kpa of the square root (hereinafter referred to asan “atmospheric pressure corrective coefficient kpa”) in the equation(32) for thereby correcting the opening command.

In the present embodiment, since the standard opening command value θ0is varied with time as described above, the standard intake pressure Pb0used in the equation (32) also varies. Thus, for accurately compensatingfor variations in the amount of intake air depending on the atmosphericpressure, it is preferable to vary the value of the standard intakepressure Pb0 depending on the standard opening command value θ0 using apredetermined data table or the like. In this embodiment, however,because any variations in the intake pressure Pb are actually smallwhile the internal combustion engine 1 is steadily operating in the FIREmode, and in view of stability of the control system, a predeterminedvalue (fixed value) is used as the standard intake pressure Pb0 in theequation (32).

In the present embodiment, moreover, in order to reduce the processingload on the controller 2, the equation (32) is not actually directlycalculated, but the following process is performed:

In each control cycle, a parameter ratio/dpa (hereinafter referred to asan “atmospheric pressure correcting parameter ratio/dpa”) defined fromthe predetermined standard atmospheric pressure Pa0, the standard intakepressure Pb0, and the atmospheric pressure Pa detected by theatmospheric pressure sensor 18 when the internal combustion engine 1starts to operate (in the start mode), i.e., the value in the squareroot sign in the equation (32), is determined by the following equation(33): $\begin{matrix}{{{ratio}/{dpa}} = \frac{{Pa0} - {Pb0}}{{Pa} - {Pb0}}} & (33)\end{matrix}$

A data table shown in FIG. 10 is prepared which contains square rootscalculated of various values of the atmospheric pressure correctingparameter ratio/dpa. The square root of the atmospheric pressurecorrecting parameter ratio/dpa which has previously been determined isdetermined as the atmospheric pressure corrective coefficient kpa. Theopening command is then corrected, i.e., multiplied, by the atmosphericpressure corrective coefficient kpa.

The atmospheric pressure corrective coefficient kpa is “1” if theatmospheric pressure Pa detected by the atmospheric pressure sensor 18is the standard atmospheric pressure Pa0, and becomes smaller as theatmospheric pressure Pa goes higher.

The basic concept of the process of compensating for variations in theamount of intake air due to the atmospheric pressure in the atmosphericcondition correcting process has been described above.

The atmospheric temperature of the atmospheric conditions will bedescribed below. As can be seen from the equation (28), the amount Gcylof intake air introduced into the combustion chamber 4 is affected bythe coefficient Ci depending on the atmospheric density, and is higheras the atmospheric density is greater. Since the atmospheric density issmaller as the atmospheric temperature is higher, the amount Gcyl ofintake air introduced into the combustion chamber 4 is smaller as theatmospheric temperature is higher.

In order to keep the amount Gcyl of intake air introduced into thecombustion chamber 4 unchanged even when the atmospheric temperaturevaries, the opening command Θ may be corrected so that the bypassopening will be greater as the atmospheric temperature is higher.

In this embodiment, a corrective coefficient kta (hereinafter referredto as an “atmospheric temperature corrective coefficient kta”) isdetermined based on an experimentally established data table shown inFIG. 11 from the atmospheric temperature Ta detected by the atmospherictemperature sensor 17 when the internal combustion engine 1 starts tooperate (in the start mode), and the opening command is corrected, i.e.,multiplied, by the atmospheric temperature corrective coefficient kta.

In this embodiment, the amount of intake air at a standard atmospherictemperature TaO (for example, 25° C.) is used as a reference. Therefore,the atmospheric temperature corrective coefficient kta is “1” when thedetected atmospheric temperature Ta is the standard atmospherictemperature Ta0, and has a higher value as the atmospheric temperatureTa is higher.

The basic concept of the process of compensating for variations in theamount of intake air due to the atmospheric temperature in theatmospheric condition correcting process has been described above.

The learning correcting process will be described below.

As described above, in order to compensate for variations in the amountof intake air due to structural factors, the SLD opening correctivequantity i/sld is determined in each control cycle according to theamount-of-intake-air F/B control correcting process using the intakeadaptive SLD control process, and the standard opening command value θ0is corrected by the SLD opening corrective quantity i/sld. If the actualamount of intake air with respect to the standard opening command valueθ0 suffer relatively large variations from a standard amount of intakeair corresponding to the standard opening command value θ0, then the SLDopening corrective quantity i/sld insofar as the integrated amount Qa ofintake air (the predicted integrated amount qair/pre of intake air) isnot converged to the target integrated amount q (the target integratedamount qair/cmd of intake air) is large, and its time-dependent changesare also large. Therefore, in the initial stage of the FIRE mode, thepattern of timedependent changes of the opening command Θ determined bycorrecting the standard opening command value θ0 with the SLD openingcorrective quantity i/sld, and hence the pattern of time-dependentchanges of the actual amount of intake air may deviate largely from thepattern of time-dependent changes of the standard opening command valueθ0 (the pattern of time-dependent changes of the target amount of intakeair).

Particularly in the initial stage of the FIRE mode (immediately afterthe internal combustion engine 1 starts to operate), the combustionstatus of the air-fuel mixture in the combustion chamber 4 tends to beunstable, and when the pattern of time-dependent changes of the openingcommand Θ deviates largely from the pattern of time-dependent changes ofthe standard opening command value θ0, the combustion and emissionstatuses of the internal combustion engine 1 may possibly be impaired.

According to the learning correcting process, the SLD opening correctivequantity i/sld determined in each control cycle while in the FIRE modeis learned, and a corrective coefficient kilearn (hereinafter referredto as a “learning corrective coefficient kilearn”) for correcting thestandard opening command value θ0 by multiplication is determined forthe entire period of operation of a next FIRE mode. The standard openingcommand value θ0 is multiplied by the learning corrective coefficientkilearn to generate an opening command Θ which exhibits stabletimedependent changes matching the pattern of time-dependent changes ofthe standard opening command value θ0.

The learning corrective coefficient kilearn is determined as follows:

From the SLD opening corrective quantity i/sld determined in eachcontrol cycle during operation of each FIRE mode, a corrective quantitygair/sld (hereinafter referred to as an “SLD intake corrective quantitygair/sld”) for the actual amount of intake air corresponding to the SLDopening corrective quantity i/sld is determined in each control cycleaccording to the following equation (34): $\begin{matrix}{{{gair}/{sld}} = {{i/{sld}} \cdot \frac{1}{Ne} \cdot {Ga2}}} & (34)\end{matrix}$

The equation (34) is similar to the equation (4) for determining actualthe amount of intake air (per TDC) corresponding to the target amountgair/cmd of intake air, i.e., the standard opening command value θ0. Ga2in the equation (34) is identical to Ga2 in the equation (4).

The SLD intake corrective quantity gair/sld is accumulated in eachcontrol cycle according to the following equation (35) to determine anintegrated value qair/sld of the SLD intake corrective quantity gair/sld(hereinafter referred to as an “SLD integrated intake correctivequantity qair/sld”):

qair/sld(k)=qair/sld(k−1)+gair/sld  (35)

Then, a value determined from the ratio (qair/sld / qair/cmd) of the SLDintegrated intake corrective quantity qair/sld to the target integratedamount qair/cmd of intake air according to the following equation (36)is determined as a basic value vpskisld of the learning correctivecoefficient kilearn (hereinafter referred to as a “basic learningcorrective coefficient vpskisld”): $\begin{matrix}{{vpskisld} = {1 + \frac{{qair}/{{sld}(k)}}{{qair}/{{cmd}(k)}}}} & (36)\end{matrix}$

The basic learning corrective coefficient vpskisld is basicallycalculated in each control cycle until the FIRE mode is finished.However, when the FIRE mode is interrupted or theignition-timing-dependent correcting process is carried out, thecalculation of the SLD opening corrective quantity i/sld is interrupted.Therefore, the calculation of the basic learning corrective coefficientvpskisld is finished before the FIRE mode is interrupted or theignition-timing-dependent correcting process is carried out, i.e.,before the learning calculation end flag f/flrnend is set to “1”.

The basic learning corrective coefficient vpskisld finally determined ineach FIRE mode is then subjected to a filtering process according to thefollowing equation (37) to determine a learning corrective coefficientkilearn for correcting the standard opening command value θ0 in a nextFIRE mode:

kilearn(j)=kilearn(j−1)·[1+Cki·(vpskisld−1)]  (37)

where kilearn(j) represents a learning corrective coefficient kilearn tobe newly determined in the present FIRE mode, kilearn(j−1) represents alearning corrective coefficient kilearn determined-in the preceding FIREmode, and Cki represents a predetermined constant of “1” or less.

If the FIRE elapsed time t/fire (which is the value of the parametert/kil established in STEP5-5, STEP5-16, etc. of the flowchart shown inFIG. 5) at the time the final basic learning corrective coefficientvpskisld is determined in each FIRE mode does not reach a predeterminedtime, then the determined basic learning corrective coefficient vpskisldis not used to determine (update) a learning corrective coefficientkilearn, but the value of the present learning corrective coefficientkilearn is maintained. This is because the reliability of the basiclearning corrective coefficient vpskisld which is produced when the FIREelapsed time t/fire is short is poor.

The basic concept of the learning correcting process has been describedabove.

The ignition-timing-dependent correcting process will be describedbelow.

As described above, when the internal combustion engine 1 is warmed upto a certain extent, i.e., when the FIRE elapsed time t/fire increasesto a certain value, the friction of various components of the internalcombustion engine 1 is gradually reduced, and the rotational speed Ne ofthe internal combustion engine 1 tends to increase. According to thepresent embodiment, in order to prevent the rotational speed Ne fromtending to increase and also to prevent the ignition timing from beingcontrolled by the ignition timing control rotational speed F/B controlprocess to become excessively retarded, the standard opening commandvalue θ0 is gradually reduced (see FIG. 7).

The manner in which the friction of various components of the internalcombustion engine 1 is reduced as the internal combustion engine 1 iswarmed up is influenced by various factors. The friction may start beinglowered more quickly than expected or may be lowered at a greater ratethan expected.

With the friction being thus reduced in varying patterns, the tendencyof the rotational speed Ne of the internal combustion engine 1 toincrease cannot sufficiently be suppressed even when the standardopening command value θ0 is gradually reduced. As a result, the ignitiontiming controlled by the ignition timing control rotational speed F/Bcontrol process reaches a retarded limit value at which the ignitiontiming can actually be controlled, and the rotational speed Ne cannot befeedback-controlled at the target rotational speed ne/fire.

The ignition-timing-dependent correcting process is a process forpreventing such a feedback control failure from occurring. Specifically,when the command value for the ignition timing which is determined bythe ignition timing control rotational speed F/B control process asdescribed later on becomes retarded beyond a certain threshold valuethat is slightly more advanced than the retarded limit value, theignition-timing-dependent correcting process corrects the standardopening command value θ0 so as to be reduced a predetermined amount ineach control cycle until such a condition disappears, i.e., until thecommand value for the ignition timing returns to an advanced valuegreater than the threshold value.

For example, while the bypass opening is being controlled according tothe standard opening command value θ0 as shown in an upper diagramsection of FIG. 12, if the command value iglog for the ignition timingdetermined according to the ignition timing control rotational speed F/Bcontrol process becomes more retarded than a threshold value IGX that isslightly greater than a retarded limit value IGLGG as shown in an areaA12 in a lower diagram section of FIG. 12, then the opening command Θ isreduced from the standard opening command value θ0 by a certaincorrective quantity θdec (hereinafter referred to as an“ignition-timing-dependent opening corrective quantity Θdec”)(Θ=θ0−θdec), as shown in the upper diagram section of FIG. 12.

As shown in an area B12 in the upper diagram section of FIG. 12, theignition-timing-dependent opening corrective quantity θdec is increaseda certain value Δθdec (>0, hereinafter referred to as an “openingreduction unit quantity Δθdec”) in each control cycle until the commandvalue iglog for the ignition timing becomes more advanced than thethreshold value IGX (see the equation in STEP15-9 shown in FIG. 15).

After the command value iglog for the ignition timing becomes moreadvanced than the threshold value IGX, as shown in an area C12 in thelower diagram section of FIG. 12, the ignition-timing-dependent openingcorrective quantity θdec is maintained at a value when the command valueiglog for the ignition timing becomes more advanced than the thresholdvalue IGX, i.e., the process of increasing the ignition-timing-dependentopening corrective quantity θdec by the opening reduction unit quantityΔθdec is stopped, and the opening command Θ is reduced from the standardopening command value θ0 by the ignition-timing-dependent openingcorrective quantity θdec.

In this embodiment, the opening reduction unit quantity Δθdec by whichto increase the ignition-timing-dependent opening corrective quantityθdec is determined based on a predetermined data table shown in FIG. 13from the engine temperature Tw at the start of the internal combustionengine 1. When the engine temperature Tw at the start of the internalcombustion engine 1 is in a high temperature range, then the frictiontends to be greater than when the engine temperature Tw is in middle andlow temperature ranges. In the data table shown in FIG. 13, the openingreduction unit quantity Δθdec is greater in the high temperature rangethan in the middle and low temperature ranges.

The basic concept of the ignition-timing-dependent correcting processhas been described above.

Based on the details described above, the process of generating thecommand value θCMD for the bypass opening (opening command), which iscarried out by the intake air quantity control means 25, in STEP4-5shown in FIG. 4 will be described in specific detail below.

As shown in FIG. 14, the value of the FIRE mode execution on/off flagf/fireon determined in each control cycle, i.e., the value establishedin the present control cycle, in the condition judgement process inSTEP4-4 (see FIG. 15) is determined in STEP14-1.

If f/fireon=1, i.e., if the operation mode is the FIRE mode, then the Nrange basic value ifiret and the D range corrective value iatfire usedto determine the standard opening command value θ0 according to thestandard opening command value generating process, the atmosphericpressure corrective coefficient kpa and the atmospheric temperaturecorrective coefficient kta used in the atmospheric condition correctingprocess, and the opening reduction unit quantity Δθdec used in theignition-timing-dependent correcting process are determined using thepredetermined data tables described above in STEP14-2.

Specifically, the N range basic value ifiret and the D range correctivevalue iatfire are determined on the basis of the data table shown inFIG. 6 from the engine temperature Tw at the start of the internalcombustion engine 1 which has been acquired in the-start mode (STEP4-2).

The atmospheric pressure correcting parameter ratio/dpa is calculatedaccording to the equation (33) from the atmospheric pressure Pa at thestart of the internal combustion engine 1 which has been acquired in thestart mode, the standard atmospheric pressure Pa0, and the standardintake pressure Pb0, and the atmospheric pressure corrective coefficientkpa (=the square root of the parameter ratio/dpa) is determined on thebasis of the data table shown in FIG. 10 from the atmospheric pressurecorrecting parameter ratio/dpa.

The atmospheric temperature corrective coefficient kta is determined onthe basis of the data table shown in FIG. 11 from the atmospherictemperature Ta at the start of the internal combustion engine 1 whichhas been acquired in the start mode.

The opening reduction unit quantity Δθdec is determined on the basis ofthe data table shown in FIG. 13 from the engine temperature Tw at thestart of the internal combustion engine 1 which has been acquired in thestart mode.

These determining processes in STEP14-2 may have been carried out inadvance in the start mode.

Then, the intake air quantity control means 25 carries out theamount-of-intake-air F/B control correcting process and theignition-timing-dependent correcting process on the standard openingcommand value θ0 to calculate a preliminary opening command θi/fire inSTEP14-3.

More specifically, as shown in FIG. 15, the inatake air quantity controlmeans 25 determines a present (present control cycle) shifted positionof the automatic transmission detected by a sensor (not shown) inSTEP15-1. If the shifted position is in the N range, then the intake airquantity control means 25 sets the basic value i/ftbl of the standardopening command value θ0 to the N range basic value ifiret determined inSTEP14-2 in STEP15-2. If the shifted position is in the D range, thenthe intake air quantity control means 25 sets the basic value i/ftbl tothe sum of the N range basic value ifiret and the D range correctivevalue iatfire determined in STEP14-2 in STEP15-3.

Then, the intake air quantity control means 25 determines the correctivecoefficient km/fire in the present control cycle based on the data tableshown in FIG. 7 from the present FIRE elapsed time t/fire in STEP15-4.The intake air quantity control means 25 multiplies the basic valuei/ftbl determined in STEP15-2 or 15-3 by the corrective coefficientkm/fire to determine the standard opening command value θ0 in STEP15-5.In this manner, the standard opening command value θ0 is determined ineach control cycle in the FIRE mode.

Then, the intake air quantity control means 25 calculates the intakedifference Eq according to a subroutine shown in FIG. 16 in STEP15-6.

As shown in FIG. 16, the intake air quantity control means 25 determinesan predicted amount gair/pre of intake air (an predicted value of theamount of intake value per TDC) in the present control cycle accordingto the equation (1) from the present intake pressure Pb detected by theintake pressure sensor 16 and the predetermined value Gal in STEP16-1.

The intake air quantity control means 25 determines whether the internalcombustion engine 1 is in the fuel cutting process or not in STEP16-2.If the internal combustion engine 1 is not in the fuel cutting process,then the intake air quantity control means 25 determines whether thepresent FIRE elapsed time t/fire has reached the SLD correction limittime TISLDLMT or not in STEP16-3.

If t/fire<TISLDLMT, then the intake air quantity control means 25forcibly sets the value of the predicted integrated amount qair/pre(k)of intake air in the present control cycle to “0” in STEP16-4. Ift/fire≧TISLDLMT, then the intake air quantity control means 25accumulates the predicted amount gair/pre of intake air to determine anpredicted integrated amount qair/pre(k) of intake air according to theequation (2) in STEP16-5.

If the internal combustion engine 1 is in the fuel cutting process inSTEP16-2, then since the air drawn into the combustion chamber 4 at thetime does not contribute to the heat energy given to the catalyticconverter 3, i.e., since the air-fuel mixture is not combusted in thecombustion chamber 4 while the internal combustion engine 1 is in thefuel cutting process, the intake air quantity control means 25 keeps thepresent value of the present predicted integrated amount qair/pre(k) ofintake air in STEP16-6.

The above processing in STEP16-1 through STEP16-6 successivelydetermines the predicted integrated amount qair/pre(k) of intake air,which corresponds to an integrated amount of heat energy actually givento the catalytic converter 3 in the FIRE mode (including itsinterruption) after it has started, from elapse of the SLD correctionlimit time TISLDLMT except when the internal combustion engine 1 is inthe fuel cutting process.

Therefore, until the SLD correction limit time TISLDLMT elapses, i.e.,immediately after the internal combustion engine 1 starts to operate,the value of the predicted integrated amount qair/pre of intake air isforcibly set to “0”.

In order to limit the value of the predicted integrated amount qair/preof intake air until the SLD correction limit time TISLDLMT elapses, thevalue of the predicted amount gair/pre of intake air may be forciblylimited to “0” until the SLD correction limit time TISLDLMT elapses, andthe equation (2) may be calculated using the limited value of thepredicted amount gair/pre of intake air. According to this process, thevalue of the predicted integrated amount qair/pre(k) of intake air isalso forcibly limited to “0” until the SLD correction limit timeTISLDLMT elapses.

After the predicted integrated amount qair/pre(k) of intake air has thusbeen determined, the intake air quantity control means 25 determines atarget amount gair/cmd of intake air in the present control cycle (atarget value for the amount of intake air per TDC) according to theequation (4) from the standard opening command value θ0 determined inSTEP15-5, the present rotational speed Ne detected by the rotationalspeed sensor 14, and a predetermined value Ga2 in STEP16-7.

The intake air quantity control means 25 makes the same decision as inSTEP16-3 in STEP16-8. If t/fire<TISLDLMT, then the intake air quantitycontrol means 25 forcibly sets the target integrated amount qair/cmd(k)of intake air in the present control cycle to “0” in STEP16-9. Ift/fire≧TISLDLMT, then the intake air quantity control means 25accumulates the target amount gair/pre of intake air in each controlcycle to determine a target integrated amount qair/cmd(k) of intake airaccording to the equation (5) in STEP16-10.

The above processing in STEP16-7 through STEP16-10 successivelydetermines the target integrated amount qair/cmd(k) of intake air, whichcorresponds to a target value of the integrated value of the amount ofheat energy actually given to the catalytic converter 3, after the FIREmode has started, from elapse of the SLD correction limit time TISLDLMT,including the interruption of the FIRE mode.

Immediately after the internal combustion engine 1 starts to operateuntil the SLD correction limit time TISLDLMT elapses, the value of thetarget integrated amount qair/cmd(k) of intake air is forcibly set to“0”, as with the predicted integrated amount qair/pre(k) of intake air.

In order to limit the value of the target integrated amount qair/cmd(k)of intake air until the SLD correction limit time TISLDLMT elapses, thevalue of the target amount gair/cmd of intake air may be forciblylimited to “0” until the SLD correction limit time TISLDLMT elapses, andthe equation (5) may be calculated using the limited value of the targetamount gair/cmd of intake air.

After the predicted integrated amount qair/pre(k) of intake air and thetarget integrated amount qair/cmd(k) of intake air have thus beendetermined, the intake air quantity control means 25 calculates theirdifference (qair/pre(k)−qair/cmd(k)) to determine the intake differenceEq(k) in the present control cycle in STEP16-11. Then, control goes backto the subroutine shown in FIG. 15.

After having determined the intake difference Eq, the intake airquantity control means 25 determines the value of a flag f/dec inSTEP15-7 shown in FIG. 15. The flag f/dec is a flag relative to theignition-timing-dependent correcting process. The flag f/dec is f/dec=1when the command value iglog for the ignition timing is more retardedthan the threshold value IGX (see FIG. 12) in a process (described lateron) of generating the command value iglog for the ignition timing, andf/dec=0 when the command value iglog for the ignition timing is moreadvanced than the threshold value IGX in the process of generating thecommand value iglog for the ignition timing. The flag f/dec willhereinafter be referred to as an “ignition timing determining flagf/dec”. The ignition timing determining flag f/dec is initialized to “0”in the start mode process (STEP4-2).

If f/dec=0, i.e., if the command value iglog for the ignition timing ismore advanced than the threshold value IGX, then the intake air quantitycontrol means 25 calculates the SLD opening corrective quantity i/sldwith respect to the amount-of-intake-air F/B control correcting processaccording to a subroutine shown in FIG. 17 in STEP15-8.

The intake air quantity control means 25 determines the present value ofthe FIRE interruption flag f/fpause in STEP17-1. If f/fpause=1, i.e., ifthe FIRE mode is to be interrupted, then the intake air quantity controlmeans 25 sets (initializes) the pole pole/i which determines the rate ofreduction of the intake difference Eq in the amount-of-intake-air F/Bcontrol correcting process to the lower limit value pole/i0 (see FIG. 9)in STEP17-2, after which control returns to the subroutine shown in FIG.15.

Therefore, while the FIRE mode is being interrupted, the SLD openingcorrective quantity i/sld is maintained at the present value (the valuebefore the FIRE mode starts being interrupted).

The SLD opening corrective quantity i/sld and the pole pole/i areinitialized respectively to “0” and “lower limit value pole/i0” in thestart mode process (STEP4-2).

If f/fpause=0, i.e., if the FIRE mode is not to be interrupted, inSTEP17-1, then the intake air quantity control means 25 determines thepole table value pole/itbl in the present control cycle based on thedata table shown in FIG. 9 from the present FIRE elapsed time t/fire inSTEP17-3.

Then, the intake air quantity control means 25 basically establishes thepole table value pole/itbl determined in STEP17-3 as the value of thepole pole/i for determining the rate of reduction of the intakedifference Eq. The intake air quantity control means 25 carries out thefollowing process for returning the pole pole/i, which has been set tothe lower limit value pole/i0 (“1” in this embodiment) while the FIREmode is being interrupted, gradually to the pole table value pole/itbldepending on the FIRE elapsed time t/fire after the interruption of theFIRE mode is canceled:

The intake air quantity control means 25 compares a value(pole/i(k−1)+ΔPOLE/I) which represents the sum of the present valuepole/i(k−1) of the pole pole/i and a preset unit incremental valueΔPOLE/I (>0) with the pole table value pole/itbl determined in STEP17-3in STEP17-4. If pole/i(k−1l)+ΔPOLE/I≧pole/itbl, then the intake airquantity control means 25 establishes the pole table value pole/itbldetermined in STEP17-3 as the value of the pole pole/i(k) in the presentcontrol cycle in STEP17-5. If pole/i(k−1)+ΔPOLE/I<pole/itbl, then theintake air quantity control means 25 establishes the value(pole/i(k−1)+ΔPOLE/I) as the value of the pole pole/i(k) in the presentcontrol cycle in STEP17-6.

After the interruption of the FIRE mode is canceled by the aboveprocess, the pole pole/i gradually returns from the lower limit valuepole/i0 to the pole table value pole/itbl depending on the FIRE elapsedtime t/fire by the unit incremental value ΔPOLE/I.

If the FIRE mode is not interrupted immediately after the internalcombustion engine 1 has started to operate, then basically the polepole/i is set to the pole table value pole/itbl, and varies as the FIREelapsed time t/fire increases in the same pattern as with the pole tablevalue pole/itbl (the unit incremental value ΔPOLE/I is established so asto vary the pole pole/i in this manner).

After having established the value of the pole pole/i, the intake airquantity control means 25 compares the value of the pole pole/i with avalue which is produced by subtracting a predetermined small valueΔPOLE/IG (>0) from a pole pole/ig established in the ignition timingcontrol rotational speed F/B control process (described later on) inSTEP17-7. The pole pole/ig is a parameter which defines the rate ofreduction of the difference between the rotational speed Ne of theinternal combustion engine 1 and the target rotational speed ne/fire inthe ignition timing control rotational speed F/B control process.

If pole/i<pole/ig−ΔPOLE/IG, then control proceeds to STEP17-9. Ifpole/i≧pole/ig−ΔPOLE/IG, then the intake air quantity control means 25sets the value of the pole pole/i forcibly to (pole/ig−ΔPOLE/IG) inSTEP17-8. Thus, the value of the pole pole/i is set to a value which isalways smaller than the pole pole/ig (<0) that is established asdescribed later on in the ignition timing control rotational speed F/Bcontrol process (more accurately, 1>|pole/i|>|pole/ig|>0). The reasonfor the above setting of the value of the pole pole/i is as follows:

In this embodiment, the intake adaptive SLD control process (feedbackcontrol process) for converging the predicted integrated amount qair/preof intake air to the target integrated amount qair/cmd of intake air,and the ignition timing control rotational speed F/B control process forconverging the rotational speed Ne of the internal combustion engine 1to the target rotational speed ne/fire are carried out independently ofeach other, and both control processes affect the rotational speed Ne ofthe internal combustion engine 1. Generally, the response of a change inthe amount of intake air with respect to a change in the bypass openingbased on the intake adaptive SLD control process is slower than theresponse of a change in the rotational speed Ne with respect to a changein the ignition timing based on the ignition timing control rotationalspeed F/B control process. Therefore, if the rate of reduction of theintake difference Eq relative to the intake adaptive SLD control processis made greater than the rate of reduction of the difference between therotational speed Ne and the target rotational speed ne/fire according tothe ignition timing control rotational speed F/B control process, bothcontrol processes interfere with each other, tending to render therotational speed Ne unstable.

In view of the above drawback, according to the present embodiment, thepole pole/i relative to the intake adaptive SLD control process isestablished such that |pole/i|>|pole/ig|, thereby making the rate ofreduction of the intake difference Eq relative to the intake adaptiveSLD control process smaller than the rate of reduction of the differencebetween the rotational speed Ne and the target rotational speed ne/fireaccording to the ignition timing control rotational speed F/B controlprocess for thereby preventing both control processes from interferingwith each other.

In STEP17-9, the intake air quantity control means 25 compares the valueof the pole pole/i with “−1”. If pole/i≦−1 (this condition may beproduced by the processing in STEP17-8), then the intake air quantitycontrol means 25 forcibly sets the value of the pole pole/i to “−1” inSTEP17-10, and then control goes to STEP17-11.

In STEP17-11, the intake air quantity control means 25 determines theswitching function σ1 from the value thus determined of the pole pole/i,the intake difference Eq(k) in the present control cycle and the intakedifference Eq(k−1) in the previous control cycle which have beendetermined in STEP15-6 according to the equation (10) (specifically, anequation similar to the equation (10) except that the coefficientparameters s1, s2 in the equation (10) are replaced respectively with“1” and “pole/i”).

Using the value of the switching function σ1, the intake air quantitycontrol means 25 calculates the equations (18), (19) (s1=1 in this case)to determine values of the reaching law input Θrch and the adaptive lawinput Θadp in the intake adaptive SLD control process in STEP17-12.Then, the intake air quantity control means 25 adds the determinedvalues of the reaching law input Θrch and the adaptive law input Θadpthereby to determine the SLD opening corrective quantity i/sld in thepresent control cycle in STEP17-13. Then, control returns to thesubroutine shown in FIG. 15.

In FIG. 15, if f/dec=1 in STEP15-7, i.e., if the present command valueiglog for the ignition timing is more retarded than the threshold valueIGX (see FIG. 12), then the intake air quantity control means 25increments the ignition-timing-dependent opening corrective quantityθdec by the opening reduction unit quantity Δθdec determined in STEP14-2in each control cycle in order to perform the ignition-timing-dependentcorrecting process in STEP15-9.

The ignition-timing-dependent opening corrective quantity θdec isinitialized to “0” in the start mode process (STEP3-2).

When the processing in STEP15-9 is carried out, the process ofdetermining the SLD opening corrective quantity i/sld is not performed,and the SLD opening corrective quantity i/sld is maintained at its valuebefore the ignition timing determining flag f/dec is set to “1”.

Then, the intake air quantity control means 25 adds the present value ofthe SLD opening corrective quantity i/sld to the standard openingcommand value θ0 and subtracts the present ignition-timing-dependentopening corrective quantity θdec therefrom for thereby calculating thepreliminary opening command θi/fire (=θ0+i/sld−θdec) based on theamount-of-intake-air F/B control correcting process and theignition-timing-dependent correcting process in STEP15-10.

Then, the intake air quantity control means 25 determines the presentvalue of the learning calculation end flag f/flrnend in STEP15-11. Whilethe FIRE mode is being carried out (while the FIRE mode execution on/offflag f/fireon is set to “1”), the learning calculation end flagf/flrnend” is set to “1” so as to finish the calculation of the basiclearning corrective coefficient vpskisld when the FIRE mode starts beinginterrupted (when the FIRE interruption flag f/fpause is set to “1”) orwhen the command value iglog for the ignition timing is more retardedthan the threshold value IGX (see FIG. 12) and theignition-timing-dependent correcting process is to begin (when theignition timing determining flag f/dec is set to “1”) (see STEP5-17shown in FIG. 5 and STEP22-8 shown in FIG. 22).

If f/flrnend=0, i.e., if the basic learning corrective coefficientvpskisld is to be calculated, then the intake air quantity control means25 calculates the basic learning corrective coefficient vpskisld asdescribed with respect to the learning correcting process in STEP15-12.

Specifically, in each control cycle, the intake air quantity controlmeans 25 determines the SLD intake corrective quantity gair/sldaccording to the equation (34) from the present SLD opening correctivequantity i/sld determined in STEP5-18, the present rotational speed Neof the internal combustion engine 1, and the predetermined value Ga2,and accumulates the determined SLD intake corrective quantity gair/sldaccording to the equation (35) thereby to determine the SLD integratedintake corrective quantity qair/sld. Then, the intake air quantitycontrol means 25 calculates the basic learning corrective coefficientvpskisld according to the equation (36) from the SLD integrated intakecorrective quantity qair/sld and the target integrated amount qair/cmdof intake air in each control cycle determined in STEP 16-10 (see FIG.16).

Until the FIRE elapsed time t/fire reaches the SLD correction limit timeTISLDLMT, since qair/cmd=0 (at this time, the SLD integrated intakecorrective quantity qair/sld is also “0”), the intake air quantitycontrol means 25 forcibly sets the value of the basic learningcorrective coefficient vpskisld to “1”.

If f/flrnend=1 in STEP15-11, i.e., if the calculation of the basiclearning corrective coefficient vpskisld is to be ended, the processingin STEP15-12 is skipped, and the basic learning corrective coefficientvpskisld is not calculated (in this case, the basic learning correctivecoefficient vpskisld determined in a control cycle before f/flrnend=1 isdetermined as its final value).

After the processing in STEP5-11, STEP5-12, the intake air quantitycontrol means 25 limits the value of the preliminary opening commandθi/fire determined in STEP15-10 to a value between predetermined upperand lower limit values (when θi/fire>the upper limit value orθi/fire<the lower limit value, the intake air quantity control means 25forcibly limits θi/fire to the upper limit value and the lower limitvalue, respectively) in STEP15-13. Thereafter, control returns to thesubroutine shown in FIG. 14.

In FIG. 14, after having determined the preliminary opening commandθi/fire, the intake air quantity control means 25 multiplies thepreliminary opening command θi/fire (=θ0+i/sld−θdec) by the atmosphericpressure corrective coefficient kpa and the atmospheric temperaturecorrective coefficient kta which have been determined in STEP14-2, andthe learning corrective coefficient kilearn determined when thepreceding FIRE mode is finished (the calculation of the learningcorrective coefficient kilearn will be described later on) for therebydetermining a command value θCMD for the bypass opening in the presentcontrol cycle in STEP14-4. Then, control goes back to the main routineshown in FIG. 3.

The processing described above serves to determine the command valueθCMD for the bypass opening in each control cycle in the FIRE mode.

If the present value of the FIRE mode execution on/off flag f/fireon is“0” in STEP14-1, i.e., if the FIRE mode is not to be carried out(basically, this is a condition after the FIRE mode is ended when theFIRE elapsed time t/fire reaches the FIRE mode limit time TFIRELMT afterthe start of the internal combustion engine 1), then the intake airquantity control means 25 determines the value of the FIRE modeexecution on/off flag f/fireon in the preceding control cycle inSTEP14-5.

If the value of the FIRE mode execution on/off flag f/fireon in thepreceding control cycle is “1”, i.e., if the FIRE mode has beenperformed up to the preceding control cycle, i.e., immediately after theFIRE mode is completed), the learning corrective coefficient kilearn forcorrecting the opening command (STEP14-4) for a next FIRE mode isdetermined (updated) from the basic learning corrective coefficientvpskisld finally determined in STEP15-12 in the preceding FIRE mode inSTEP14-6 according to a subroutine shown in FIG. 18.

As shown in FIG. 18, the intake air quantity control means 25 determineswhether or not the learning end time parameter t/kil representing theFIRE elapsed time t/fire at the time the calculation of the basiclearning corrective coefficient vpskisld is finally ended is greaterthan or equal to a predetermined value TMKILLMT in STEP18-1. As shown inFIG. 5, the learning end time parameter t/kil is the FIRE elapsed timet/fire when the learning calculation end flag f/flrnend switches from“0” to “1”. When the FIRE mode is interrupted, the learning end timeparameter t/kil is the FIRE elapsed time t/fire at the start of theinterruption of the FIRE mode. When the ignition-timing-dependentcorrecting process is carried out during the FIRE mode, the learning endtime parameter tikil is the FIRE elapsed time t/fire at the start of theignition-timing-dependent correcting process. When the FIRE mode isended without the interruption of the FIRE mode or theignition-timing-dependent correcting process, the learning end timeparameter t/kil is the FIRE elapsed time t/fire, which is usually theFIRE mode limit time TFIRELMT, at the end of the FIRE mode.

Stated otherwise, the learning end time parameter t/kil is the FIREelapsed time t/fire in which the calculation of the SLD openingcorrective quantity i/sld and the corresponding correction of thestandard opening command value θ0 are continuously carried out.

If t/kil<TMRKILLMT in STEP18-1, then since the reliability of thefinally obtained basic learning corrective coefficient vpskisld isconsidered to be poor, the learning corrective coefficient kilearn ismaintained at the present value, and control returns to the subroutineshown in FIG. 14.

If t/kil−TMKILLMT, i.e., if the calculation of the SLD openingcorrective quantity i/sld and the corresponding correction of thestandard opening command value θ0 are continuously carried out for acertain long period of time, a new learning corrective coefficientkilearn(j) is determined by the filtering process represented by theequation (37) from the basic learning corrective coefficient vpskisldfinally obtained in the FIRE mode performed up to the preceding controlcycle in STEP18-2. After the learning corrective coefficient kilearn(j)is forcibly limited to a value between predetermined upper and lowerlimit values (if kilearn(j)>the upper limit value, kilearn(j) isforcibly limited to the upper limit value, and if kilearn(j)>the lowerlimit value, kilearn(j) is forcibly limited to the lower limit value) inSTEP18-3, control returns to the subroutine shown in FIG. 14.

The learning corrective coefficient kilearn(j) has an initial value of“1”. The value of the learning corrective coefficient kilearn(j) isstored in a nonvolatile memory such as an EEPROM or the like so that itwill not be lost even when the system is out of operation.

In FIG. 14, if the value of the FIRE mode execution on/off flag f/fireonin the preceding control cycle is “1” in STEP14-5, then the learningcorrective coefficient kilearn is updated. If the value of the FIRE modeexecution on/off flag f/fireon in the preceding control cycle is “0”,then since the learning corrective coefficient kilearn has already beenupdated, the processing in STEP14-6 is skipped. Therefore, the learningcorrective coefficient kilearn is updated only in a control cycleimmediately after the FIRE mode is ended, and the updated learningcorrective coefficient kilearn is used to correct the opening commandfor a next FIRE mode.

After having performing the processing in STEP14-5, STEP14-6, the intakeair quantity control means 25 sets the opening command θCMD to anopening command for the normal mode in STEP14-7. This opening command issmaller than the opening command θCMD in the FIRE mode, and set to agiven value for normally operating the internal combustion engine 1.

The processing described above with reference to FIGS. 14 through 18 isa detailed process for generating the opening command (the command valuefor the bypass opening) θCMD in each control cycle in STEP4-5 shown inFIG. 4.

The opening command θCMD thus generated is given to the bypass valveactuator 24, which controls the opening of the bypass valve 7 accordingto the given opening command θCMD.

The process of generating the command value iglog for the ignitiontiming in STEP4-6 shown in FIG. 4 will be described below.

Prior to describing specific details of this process, a basic concept ofthe process will first be described below.

In the system according to the present embodiment, since the rotationalspeed Ne (actual rotational speed) of the internal combustion engine 1tends to rise due to the above control process for increasing the amountof intake air in the FIRE mode, the rotational speed Ne isfeedback-controlled at the target rotational speed ne/fire according tothe ignition timing control rotational speed F/B control process to makethe ignition timing retarded (the ignition timing control rotationalspeed F/B control process). At this time, as described later on, it ispreferable that the rate of reduction (corresponding to the gain of thefeedback control) of the difference between the rotational speed Ne andthe target rotational speed ne/fire be established variably.

To this end, in the ignition timing control rotational speed F/B controlprocess in the system according to the present embodiment, a slidingmode control process (an adaptive sliding mode control process accordingto this embodiment) which is a response designating control processcapable of setting the rate of reduction of the difference to a desiredrate, is employed as with the amount-of-intake-air F/B controlcorrecting process.

In the present embodiment, an algorithm of the ignition-timing controlrotational speed F/B control correcting process using the adaptivesliding mode control process (hereinafter referred to as an “ignitiontiming adaptive SLD control process”), e.g., the process of generatingthe command value iglog for the ignition timing to converge therotational speed Ne to the target rotational speed ne/fire, isconstructed as follows:

In this embodiment, an object to be controlled by the ignition timingadaptive SLD control process is considered to be a system for generatingdata representing the rotational speed Ne (actual rotational speed) fromdata representing the command value iglog for the ignition timing, andis expressed by a discrete-system (discrete-time system) model.

The difference DIG (=iglog−ig0, hereinafter referred to as an “ignitiontiming difference command value DIG”) between the command value iglogfor the ignition timing and a predetermined reference command value ig0is used as data representing the command value iglog for the ignitiontiming, and the difference DNE (=Ne−Ne0, hereinafter referred to as a“difference rotational speed DNE”) between the rotational speed Ne and apredetermined reference rotational speed Ne0 is used as datarepresenting the rotational speed Ne.

The basic command value igbase (the command value for the ignitiontiming in the normal mode of operation of the internal combustion engine1 other than the FIRE mode) shown in FIG. 3 is used as the referencecommand value ig0 for the ignition timing (ig0=igbase). Therefore, thecorrective quantity DIG shown in FIG. 3 is the above ignition timingdifference command value DIG. In this embodiment, the idling rotationalspeed NOBJ shown in FIG. 3 is used as the reference rotational speedrelative to the rotational speed Ne (Ne0=NOBJ).

Using the ignition timing difference command value DIG and thedifference rotational speed DNE, the model to be controlled by theignition timing adaptive SLD control process is expressed by adiscrete-system (discrete-time system) model (secondary autoregressivemodel) as represented by the following equation (38):

DNE(k+1)=c1·DNE(k)+c2·DNE(k−1)+d1·DIG(k)  (38)

The model to be controlled as represented by the equation (38)(hereinafter referred to as a “rotational speed controlled model”)expresses a difference rotational speed DNE(k+1) in each control cycleas an output of the rotational speed controlled model, using pasttime-series data DNE(K), DNE(k−1) of the difference rotational speed DNEand an ignition timing difference command value DIG(k) as an input ofthe rotational speed controlled model.

In the equation (38), coefficients c1, c2 relative to the respectivedifference rotational speeds DNE(K), DNE(k−1) and a coefficient d1relative to the ignition timing difference command value DIG(k) aremodel parameters which define the actual behavioral characteristics ofthe rotational speed controlled model. These model parameters c1, c2, d1are identified by experimentation and simulation so that the behavioralcharacteristics of the rotational speed controlled model and thebehavioral characteristics of an actual controlled object expressed bythe rotational speed controlled model will match each other.

Since the rotational speed controlled model is a discrete-system model,it is possible to identify the model parameters c1, c2, d1 relativelyeasily by using various known identifying algorithms, e.g., an algorithmfor identifying the model parameters c1, c2, d1 according to the methodof least squares in order to minimize the error between the differencerotational speed DNE(k+1) generated on the rotational speed controlledmodel and the actual difference rotational speed.

Based on the rotational speed controlled model thus constructed, analgorithm of the ignition timing adaptive SLD control process isconstructed as follows:

In the ignition timing adaptive SLD control process, as in the intakeadaptive sliding mode control process, a switching function σ2 requiredfor the sliding mode control process is defined by a linear functionaccording the equation (39), shown below, where time-series data En(k),En(k−1) in each control cycle of the difference En=DNE−dne (hereinafterreferred to as a “rotational speed difference En”) between thedifference rotational speed DNE and its target value dne are variables.The target value dne for the difference rotational speed DNE(hereinafter referred to as a “difference target rotational speed dne”)is the difference (=ne/fire−Ne0) between the target rotational speedne/fire shown in FIG. 3 and the reference rotational speed Ne0 (=idlingrotational speed NOBJ). Therefore, the rotational speed differenceEn=DNE−dne is the same as the difference (=Ne−ne/fire) between therotational speed Ne (actual rotational speed) and the target rotationalspeed ne/fire. $\begin{matrix}\begin{matrix}{{{\sigma 2}(k)} = \quad {{{s3} \cdot ( {{{DNE}(k)} - {{dne}(k)}} )} + {{s4} \cdot}}} \\{\quad ( {{{DNE}( {k - 1} )} - {{dne}( {k - 1} )}} )} \\{= \quad {{{s3} \cdot {{En}(k)}} + {{s4} \cdot {{En}( {k - 1} )}}}}\end{matrix} & (39)\end{matrix}$

where s3, s4 represent coefficient parameters of the terms of theswitching function σ2, and are established to satisfy the followingcondition: $\begin{matrix}{{{- 1} < \frac{s4}{s3} < 1}( {{{{when}\quad {s3}} = 1},{{- 1} < {s4} < 1}} )} & (40)\end{matrix}$

In the present embodiment, s3=1 for the sake of brevity. The value ofthe coefficient parameter s4 (more generally, the value ofs4/s3=pole/ig) is established variably, as described later on.

With the switching function σ2 defined as described above, as in theintake adaptive sliding mode control process, if state quantities(En(k), En(k−1)) comprising the set of the time-series data En(k),En(k−1) of the rotational speed difference En are converged onto aswitching curve defined by a2=0 and remain converged, then the statequantities (En(k), En(k−1)) can be converged to a balanced point on theswitching curve σ2=0, i.e., a point where En(k)=En(k−1)=0, highly stablywithout being affected by disturbances.

In order to converge the difference rotational speed DNE to thedifference target rotational speed dne, i.e., to converge the rotationalspeed Ne to the target rotational speed ne/fire, a control inputgenerated by the ignition timing adaptive SLD control process as aninput to be applied to the object to be controlled, which is modeledaccording to the equation (39), i.e., the ignition timing differencecommand value DIG, is the sum of an equivalent control input DIGeq, areaching law input DIGrch, and an adaptive law input DIGadp, as in theintake adaptive sliding mode control process (see the following equation(41)).

DIG(k)=DIGeq(k)+DIGrch(k)+DIGadp(k)  (41)

As in the intake adaptive sliding mode control process, the equivalentcontrol input DIGeq, the reaching law input DIGrch, and the adaptive lawinput DIGadp are given by the respective following equations (42)through (44): $\begin{matrix}\begin{matrix}{{{DIGeq}(k)} = \quad {\frac{- 1}{{s3} \cdot {d1}} \cdot \lbrack {{( {{{s3} \cdot ( {c - 1} )} + {s4}} ) \cdot {{DNE}(k)}} +} }} \\{\quad {{( {{{s3} \cdot {c2}} - {s4}} ) \cdot {{DNE}( {k - 1} )}} - {{s3} \cdot ( {{{dne}( {k + 1} )} -} }}} \\{ \quad {{dne}(k)} ) -  {{s4} \cdot ( {{{dne}(k)} - {{dne}( {k - 1} )}} )} \rbrack} \\{= \quad {\frac{- 1}{{s3} \cdot {d1}} \cdot \lbrack {{( {{{s3} \cdot ( {{c1} - 1} )} + {s4}} ) \cdot {{En}(k)}} +} }} \\{{\quad  {( {{{s3} \cdot {c2}} - {s4}} ) \cdot {{En}( {k - 1} )}} \rbrack} + {\frac{- 1}{d1} \cdot}} \\{\quad \lbrack {{- {{dne}( {k + 1} )}} + {{c1} \cdot {{dne}(k)}} + {{c2} \cdot {{dne}( {k - 1} )}}} \rbrack}\end{matrix} & (42) \\{{{DIGrch}(k)} = {\frac{- 1}{{s3} \cdot {d1}} \cdot {F3} \cdot {{\sigma 2}(k)}}} & (43) \\{{{DIGadp}(k)} = {\frac{- 1}{{s3} \cdot {d1}} \cdot {F4} \cdot {\sum\limits_{i = 0}^{k}{{\sigma 2}(i)}}}} & (44)\end{matrix}$

A coefficient F3 in the equation (43), i.e., a coefficient for defininga gain relative to the reaching law, is established to satisfy theinequality (45) or more preferably (45)′ shown below.

A coefficient F4 in the equation (44), i.e., a coefficient for defininga gain relative to the adaptive law, is established to satisfy theinequality (46) shown below where ΔT represents a control cycle (controlperiod).

0<F3<2  (45)

0<F3<1  (45)′

$\begin{matrix}{{F4} = {J^{\prime} \cdot \frac{2 - {F3}}{\Delta \quad T}}} & (46)\end{matrix}$

 (0<J′<2)

In the ignition timing adaptive SLD control process, the equivalentcontrol input DIGeq, the reaching law input DIGrch, and the adaptive lawinput DIGadp are determined according to the equations (42) through (44)in each control cycle, and their sum is calculated according to theequation (41) thereby to determine the ignition timing differencecommand value DIG. The ignition timing difference command value DIG isadded to the reference command value ig0, i.e., the basic command valueigbase in the normal operation of the internal combustion engine 1,according to the following equation (47) thereby to determine thecommand value iglog for the ignition timing: $\begin{matrix}\begin{matrix}{{{iglog}(k)} = \quad {{{igbase}(k)} + {{DIG}(k)}}} \\{= \quad {{{igbase}(k)} + ( {{{DIGeq}(k)} + {{DIGrch}(k)} + {{DIGadp}(k)}} )}}\end{matrix} & (47)\end{matrix}$

The difference rotational speed dne required to determine the equivalentcontrol input DIGeq and the value of the switching function σ2 isdetermined as follows:

In this embodiment, when the rotational speed Ne (actual rotationalspeed) of the internal combustion engine 1 reaches the preset rotationalspeed (=NOBJ+NEFSLDS) shown in FIG. 3, or when the FIRE elapsed timet/fire reaches the predetermined value TSLDIGST, the ignition timingcontrol rotational speed F/B control. process is started. The targetrotational speed ne/fire of the internal combustion engine 1 in the FIREmode is determined according to the following equation (48) depending onan elapsed time Δt/nfb (hereinafter referred to as a “rotational speedF/B elapsed time Δt/nfb”) from the start of the ignition timing controlrotational speed F/B control process: $\begin{matrix}{{{ne}/{{fire}(k)}} = {{NOBJ} + {NEFSLDS} - {{{K/{NE}} \cdot \Delta}\quad {t/{{nfb}( {{{{if}\quad \Delta \quad {t/{nfb}}} \geq \frac{NEFSLDS}{K/{NE}}},{{{then}\quad {{ne}/{{fire}(k)}}} = {NOBJ}}} )}}}}} & (48)\end{matrix}$

where K/NE represents a predetermined value (>0) which defines thedegree at which the target rotational speed ne/fire decreases with time(gradient).

If the calculated result of the right-hand side of the equation (48) islower than the idling rotational speed NOBJ (Δt/nfb>NEFSLDS/K/NE), thenthe target rotational speed ne/fire is fixed to the idling rotationalspeed NOBJ.

Thus, after the ignition timing control rotational speed F/B controlprocess has started, the target rotational speed ne/fire graduallydecreases linearly from the preset rotational speed (=NOBJ+NEFSLDS)toward the idling rotational speed NOBJ. After the target rotationalspeed ne/fire has reached the idling rotational speed NOBJ, the targetrotational speed ne/fire is maintained at the idling rotational speedNOBJ.

Therefore, the target rotational speed ne/fire(k) in each control cycleis determined from the rotational speed F/B elapsed time Δt/nfb in thecontrol cycle according to the equation (48). By subtracting the idlingrotational speed NOBJ from the target rotational speed ne/fire(k), thedifference target rotational speed dne(k) (=ne/fire(k)−NOBJ) in eachcontrol cycle is determined. Using the difference target rotationalspeed dne(k) and its preceding value dne(k−1) (=ne/fire(k−1)−NOBJ),i.e., the difference target rotational speed dne(k−1) determined in thepreceding control cycle, the value of the switching function σ2 (k) canbe determined in each control cycle according to the equation (39).Using the value of the switching function σ2, the reaching law inputDIGrch and the adaptive law input DIGadp can be determined according tothe respective equations (43), (44).

In this embodiment, since the control cycle (TDC) is inverselyproportional to the rotational speed Ne, the rotational speed F/Belapsed time (=Δt/nfb+ΔT) in a next control cycle can be predicted(hereinafter referred to as a “rotational speed F/B predicted elapsedtime Δt/nfbpre”) by determining a time ΔT (∝1/Ne) of one control cyclefrom the present rotational speed Ne and adding the time ΔT to thepresent rotational speed F/B elapsed time Δt/nfb. By applying therotational speed F/B predicted elapsed time Δt/nfbpre to the equation(48), i.e., putting Δt/nfbpre in Δt/nfb in the right-hand side of theequation (48), it is possible to determine a target rotational speedne/fire(k+1) in the next control cycle according to the followingequation (49): $\begin{matrix}{{{ne}/{{fire}( {k + 1} )}} = {{NOBJ} + {NEFSLDS} - {{{K/{NE}} \cdot \Delta}\quad {t/{{nfbpre}( {{{{if}\quad \Delta \quad {t/{nfpre}}} \geq \frac{NEFSLDS}{K/{NE}}},{{{then}\quad {{ne}/{{fire}( {k + 1} )}}} = {NOBJ}}} )}}}}} & (49)\end{matrix}$

By subtracting the idling rotational speed NOBJ from the targetrotational speed ne/fire(k+1), it is possible to determined a differencetarget rotational speed dne(k+1) (32 ne/fire(k+1)−NOBJ) in the nextcontrol cycle.

So it is possible to determine the equivalent control input DIGeq, byapplying the difference target rotational speed dne(k+1), dne(k) anddne(k−1) determined as above to the equation (42)

While the FIRE mode is being interrupted, the ignition timing controlrotational speed F/B control process is interrupted, and the commandvalue iglog for the ignition timing is returned to the basic commandvalue igbase in the normal operation of the internal combustion engine1. Specifically, after the start of the interruption of the FIRE mode,the value (absolute value) of the ignition timing difference commandvalue DIG according to the equation (47) is reduced by a predeterminedunit value dec/ig in each control cycle until it becomes “0”, i.e.,gradually reduced to “0”, for thereby returning the command value iglogfor the ignition timing gradually to the basic command value igbase.When the interruption of the FIRE mode is canceled, the ignition timingcontrol rotational speed F/B control process is immediately resumed.

In this embodiment, the command value iglog for the ignition timing isgradually returned to the basic command value igbase also when the FIREmode is ended (the FIRE mode execution on/off flag f/fireon changes from“1” to “0”) and the operation mode of the system is shifted to thenormal mode.

The basic concept of the ignition timing control rotational speed F/Bcontrol process has been described above.

In the ignition timing adaptive SLD control process which is a responsedesignating control process, the rate of reduction of the rotationalspeed difference En (=DNE−dne=Ne−ne/fire) can be designated by the valueof the ratio (s4/s3) (hereinafter referred to as a “pole pole/ig”) ofthe coefficient parameters s3, s4 of the switching function σ2. As theabsolute value of the pole pole/ig (=s4/s3) approaches “0” within arange smaller than “1”, the rate of reduction of the rotational speeddifference En becomes higher. As with the intake adaptive SLD controlprocess, s4/s3=pole/ig<0 in order to avoid an oscillatory attenuation ofthe rotational speed difference En.

In this embodiment, using the response designating characteristics ofthe ignition timing adaptive SLD control process, the rate of reductionof the rotational speed difference En is established variably asfollows:

A change in the rotational speed Ne of the internal combustion engine 1with respect to a change in the ignition timing tends to be greater asthe ignition timing is more retarded. Therefore, in order to control therotational speed Ne stably at the target rotational speed ne/fire, it ispreferable that the rate of reduction of the rotational speed differenceEn be lower (the absolute value of the pole pole/ig be greater) as theignition timing which is controlled is more retarded.

In each control cycle, therefore, a basic value pole/igtbl of the polepole/ig is determined based on a data table shown in FIG. 19 from thepresent command value iglog for the ignition timing (the command valueiglog determined in the preceding control cycle) in each control cycle,and the basic value pole/igtbl is established as the value of the polepole/ig. The basic value pole/igtbl (hereinafter referred to as an“ignition-timing-dependent pole basic value pole/igtbl”) is establishedsuch that its absolute value |pole/igtbl| is greater as the commandvalue iglog for the ignition timing is more retarded (−1<pole/igtbl<0).

The ignition-timing-dependent pole basic value pole/igtbl is basicallyestablished so as to be closer to “0” than the pole table valuepole/itbl determined by the data table shown in FIG. 9 with respect tothe intake adaptive SLD control process. Stated otherwise, theignition-timing-dependent pole basic value pole/igtbl is establishedsuch that the rate of reduction of the rotational speed difference Endefined by the ignition-timing-dependent pole basic value pole/igtbl inrelation to the ignition timing adaptive SLD control process is greaterthan the rate of reduction of the intake difference Eq defined by thepole table value pole/itbl in relation to the intake adaptive SLDcontrol process.

In this embodiment, before the ignition timing control rotational speedF/B control process is started, if the ignition timing is variedabruptly in order to converge the rotational speed Ne to the targetrotational speed ne/fire according to the ignition timing adaptive SLDcontrol process, then the combustion status of the internal combustionengine 1 may possibly be impaired. Therefore, in an initial stage of theignition timing control rotational speed F/B control process, the valueof the pole pole/ig should preferably be established to make the rate ofreduction of the rotational speed difference En somewhat slow.

Consequently, in each control cycle, a corrective coefficient kigt forcorrecting (by multiplication) the ignition-timing-dependent pole basicvalue pole/igtbl depending on the rotational speed F/B elapsed timeΔt/nfb is determined based on a predetermined data table (time table)shown in FIG. 20 from the rotational speed F/B elapsed time Δt/nfb (thetime elapsed from the start of the ignition timing control rotationalspeed F/B control process). Then, the ignition-timing-dependent polebasic value pole/igtbl is corrected by being multiplied by thecorrective coefficient kigt (hereinafter referred to as a “timedependentcorrective coefficient kigt”).

In the data table shown in FIG. 20, in an initial stage of the ignitiontiming control rotational speed F/B control process, i.e., until therotational speed F/B elapsed time Δt/nfb reaches a predetermined valueT/NFBX, the time-dependent corrective coefficient kigt is determined tobe of a value (>1) so as to correct the ignition-timing-dependent polebasic value pole/igtbl in a direction to slightly increase the absolutevalue of the ignition-timing-dependent pole basic value pole/igtb1,i.e., in a direction to lower the rate of reduction of the rotationalspeed difference En. The time-dependent corrective coefficient kigt isalso established such that it is of a greater value as the rotationalspeed F/B elapsed time Δt/nfb is shorter. Therefore, theignition-timing-dependent pole basic value pole/igtbl is corrected so asto increase the absolute value of the ignition-timing-dependent polebasic value pole/igtbl, i.e., to lower the rate of reduction of therotational speed difference En, as the rotational speed F/B elapsed timeΔt/nfb is shorter. After the rotational speed F/B elapsed time Δt/nfbhas reached the predetermined value T/NFBX, the time-dependentcorrective coefficient kigt is maintained at “1”, and theignition-timing-dependent pole basic value pole/igtbl is not corrected.

Furthermore, while the FIRE mode is being interrupted, the ignitiontiming control rotational speed F/B control process is interrupted, andthe rotational speed Ne is not feedback-controlled. Consequently, theinterruption of the FIRE mode is canceled. When the ignition timingcontrol rotational speed F/B control process is resumed, the rotationalspeed Ne of the internal combustion engine 1 may possibly be much higherthan the target rotational speed ne/fire. However, since the rotationalspeed difference En is large in this condition, the command value iglogfor the ignition timing determined as described above according to theignition timing control rotational speed F/B control process abruptlybecomes excessively retarded, resulting in an impaired combustion statusof the internal combustion engine 1. Accordingly, when the ignitiontiming control rotational speed F/B control process is resumed bycanceling the interruption of the FIRE mode, as long as the rotationalspeed Ne of the internal combustion engine 1 is much higher than thetarget rotational speed ne/fire, it is preferable to reduce the rate ofreduction of the rotational speed difference En and avoid thedetermination of the ignition timing difference command value DIG whichwould make the command value iglog for the ignition timing excessivelyretarded.

Therefore, in each control cycle, a corrective coefficient kigne(hereinafter referred to as a “rotational-speed-dependent correctivecoefficient kigne”) for correcting (by multiplication) theignition-timing-dependent pole basic value pole/igtbl dependent on therotational speed Ne is determined based on a predetermined data tableshown in FIG. 21 from the present rotational speed Ne of the internalcombustion engine 1 in each control cycle. In the data table shown inFIG. 21, the rotational-speed-dependent corrective coefficient kigne isbasically determined to be of a value (>1) so as to correct theignition-timing-dependent pole basic value pole/igtbl in a direction toincrease the absolute value of the ignition-timing-dependent pole basicvalue pole/igtbl, i.e., in a direction to lower the rate of reduction ofthe rotational speed difference En, as the rotational speed Ne ishigher, i.e., as the rotational speed Ne is higher than the targetrotational speed ne/fire. In order to correct theignition-timing-dependent pole basic value pole/igtbl for apredetermined period XCNT, which is an initial value of the count-downtimer cnt/igvpl in STEP5-18 shown in FIG. 5, after the ignition timingcontrol rotational speed F/B control process is resumed, therotational-speed-dependent corrective coefficient kigne is correctedaccording to the equation (50), shown below. Theignition-timing-dependent pole basic value pole/igtbl is corrected bybeing multiplied by the corrected rotational-speed-dependent correctivecoefficient kignef (hereinafter referred to as a“rotational-speed-dependent corrected corrective coefficient kignef”).$\begin{matrix}{{kignef} = {1 + {( {{kigne} - 1} ) \cdot \frac{{cnt}/{igvpl}}{XCNT}}}} & (50)\end{matrix}$

The count-down timer cnt/igvpl in the equation (50) is set to thepredetermined period XCNT at all times during the interruption of theFIRE mode (FIRE interruption flag f/fpause=1) in STEP5-18 shown in FIG.5. When the ignition timing control rotational speed F/B control processis resumed by canceling the interruption of the FIRE mode, the value ofthe count-down timer cnt/igvpl decremented by a predetermined value fromthe value of the predetermined period XCNT in each control cycle untilfinally it becomes “0”, after which the count-down timer cnt/igvpl ismaintained at “0”. Therefore, the rotational-speed-dependent correctedcorrective coefficient kignef determined by the equation (50) is of avalue (≧1) dependent on the rotational speed Ne after the ignitiontiming control rotational speed F/B control process is resumed until thepredetermined period XCNT elapses. After elapse of the predeterminedperiod XCNT, kignef=1 (at this time, the ignition-timing-dependent polebasic value pole/igtbl is not corrected by therotational-speed-dependent corrected corrective coefficient kignef.

The count-down timer cnt/igvpl is initialized to “0” in the start modeprocess (STEP3-2), and is maintained at “0” during the interruption ofthe FIRE mode and after the interruption of the FIRE mode is ended untilthe predetermined period XCNT elapses.

In this embodiment, in each control cycle, a value produced bymultiplying the ignition-timing-dependent pole basic value pole/igtbldetermined as described above by the time-dependent correctivecoefficient kigt and the rotational-speed-dependent corrected correctivecoefficient kignef according to the following equation (51) isestablished as the final value of the pole pole/ig:

pole/ig=pole/igtbl·kigt·kignef  (51)

The time-dependent corrective coefficient kigt is kigt>1 only in aninitial stage right after the start of the ignition timing controlrotational speed F/B control process, and kigt=1 otherwise. Therotational-speed-dependent corrected corrective coefficient kignef iskignef>1 only in an initial stage immediately after the interruption ofthe FIRE mode is canceled and when the rotational speed Ne is relativelyhigh, and kignef=1 otherwise. Therefore, the value of the pole pole/igestablished by the equation (51) is normally represented by theignition-timing-dependent pole basic value pole/igtbl.

Based on the details described above, the process of generating thecommand value iglog for the ignition timing, which is carried out by theignition timing control means 26 in STEP4-6, will be described inspecific detail below.

The processing in STEP4-6 is illustrated as a subroutine shown in FIG.22. As shown in FIG. 22, the ignition timing control means 26 firstdetermines a basic command value igbase for the ignition timing inSTEP22-1. The basic command value igbase is determined according topredetermined maps and equations from the present rotational speed Ne,the intake pressure Pb, the engine temperature Tw, and the atmospherictemperature Ta, etc.

Then, the ignition timing control means 26 carries out a process ofdetermining the ignition timing difference command value DIG accordingto a subroutine shown in FIG. 23 in STEP22-2.

First, the ignition timing control means 26 determines the present valueof the FIRE mode execution on/off flag f/fireon in STEP23-1.

If f/fireon=1, i.e., if the FIRE mode is to be carried out, then theignition timing control means 26 determines the value of a flag f/nefb(hereinafter referred to as a “rotational speed F/B execution on/offflag f/nefb”) in STEP23-2. The rotational speed F/B execution on/offflag f/nefb is “1” when the ignition timing control rotational speed F/Bcontrol process is to be performed, and “0” when the ignition timingcontrol rotational speed F/B control process is not to be performed.

The rotational speed F/B execution on/off flag f/nefb is initialized to“0” in the start mode process (STEP4-2).

If f/nefb=0, i.e., if the ignition timing control rotational speed F/Bcontrol process is not to be performed, in STEP23-2, then the ignitiontiming control means 26 initializes the rotational speed F/B elapsedtime Δt/nfb to “0” in STEP23-3. The rotational speed F/B elapsed timeΔt/nfb starts being measured from a control cycle in which f/nefb=1 inSTEP23-2 and the ignition timing control rotational speed F/B controlprocess is to be performed. If f/nefb=1 in STEP23-2, the processing inSTEP23-3 is skipped.

Then, the ignition timing control means 26 determines a targetrotational speed ne/fire(k) in the present control cycle and a targetrotational speed ne/fire(k+1) in the next control cycle in STEP23-4. Thetarget rotational speed ne/fire(k) in the present control cycle isdetermined from the present rotational speed F/B elapsed time Δt/nfbaccording to the equation (48). The target rotational speed ne/fire(k+1)in the next control cycle is determined as follows: The time ΔT of onecontrol cycle recognized from the present rotational speed Ne of theinternal combustion engine 1 (the detected value of the rotational speedsensor 14) is added to the present rotational speed F/B elapsed timeΔt/nfb thereby to determine a rotational speed F/B predicted elapsedtime Δt/nfbpre, and the target rotational speed ne/fire(k+1) isdetermined from the rotational speed F/B predicted elapsed timeΔt/nfbpre according to the equation (49).

The target rotational speed ne/fire(k) in the present control cycle isthe preset rotational speed (NOBJ+NEFSLDS) while the rotational speedF/B elapsed time Δt/nfb is being set to “0” (f/nefb=0) in STEP23-3.

Then, the ignition timing control means 26 determines whether or not thepresent rotational speed Ne is equal to or higher than the presenttarget rotational speed ne/fire(k) in STEP23-5, and then whether or notthe present FIRE elapsed time t/fire is equal to or greater than thepredetermined value TSLDIGST in STEP23-6.

If either one of the conditions in STEP23-5, STEP23-6 is satisfied, thenthe ignition timing control means 26 sets the value of the rotationalspeed F/B execution on/off flag f/nefb to “1” in STEP23-7. Thus, afterthe FIRE mode has started, when the rotational speed Ne reaches thepreset rotational speed (NOBJ+NEFSLDS) or when the FIRE elapsed timet/fire reaches the predetermined value TSLDIGST, the rotational speedF/B execution on/off flag f/nefb is set to “1”, making it possible toperform the ignition timing control rotational speed F/B controlprocess.

If neither one of the conditions in STEP23-5, STEP23-6 is satisfied,then the processing in STEP23-7 is skipped, and the rotational speed F/Bexecution on/off flag f/nefb is maintained at “0”. After the rotationalspeed F/B execution on/off flag f/nefb has been set to “1”, it will notbe returned to “0” while in the FIRE mode.

Then, the ignition timing control means 26 calculates the presentrotational speed difference En(k) (=Ne−ne/fire(k)) in the presentcontrol cycle from the present rotational speed Ne and the presenttarget rotational speed ne/fire(k) determined in STEP23-4 in STEP23-8.

Thereafter, the ignition timing control means 26 determines the value ofthe FIRE interruption flag f/fpause in STEP23-9. If f/fpause=0, i.e., ifthe FIRE mode is not to be interrupted, then the ignition timing controlmeans 26 determines the value of the rotational speed F/B executionon/off flag f/nefb in STEP23-10.

If f/nefb=0, then the ignition timing control means 26 sets the value ofthe ignition timing difference command value DIG(k) in the presentcontrol cycle to “0” in STEP23-11. Thereafter, control returns to thesubroutine shown in FIG. 22.

If f/nefb=1 in STEP23-10, then the ignition timing control means 26calculates the ignition timing difference command value DIG(k) for theignition timing control rotational speed F/B control process inSTEP23-12.

The ignition timing difference command value DIG(k) is calculated asfollows:

In a subroutine shown in FIG. 24, the ignition timing control means 26determines the ignition-timing-dependent pole basic value pole/igtblaccording to the data table shown in FIG. 19 from the present commandvalue iglog(k−1) for the ignition timing (the command value determinedin the preceding control cycle) in STEP24-1.

The ignition timing control means 26 determines the time-dependentcorrective coefficient kigt from the present rotational speed F/Belapsed time Δt/nfb according to the data table shown in FIG. 20 inSTEP24-2.

The ignition timing control means 26 determines therotational-speed-dependent corrective coefficient kigne from the presentrotational speed Ne according to the data table shown in FIG. 21 inSTEP24-3. Then, the ignition timing control means 26 determines therotational-speed-dependent corrected corrective coefficient kignefaccording to the equation (50) from the rotational-speed-dependentcorrective coefficient kigne, the present value of the count-down timercnt/igvpl, and the predetermined period XCNT determined as the initialvalue of the count-down timer cnt/igvpl after the end of theinterruption of the FIRE mode in STEP24-4.

The ignition timing control means 26 multiplies theignition-timing-dependent pole basic value pole/igtbl determined inSTEP24-1 by the time-dependent corrective coefficient kigt determined inSTEP24-2 and the rotational-speed-dependent corrected correctivecoefficient kignef determined in STEP24-4, i.e., calculates the equation(51), for thereby determining the value of the pole pole/ig in thepresent control cycle in STEP24-5.

Thereafter, the ignition timing control means 26 determines theswitching function σ2(k) in the present control cycle according to theequation (39) from the rotational speed differences En(k), En(k−1)determined in STEP23-8 in the present and preceding control cycles andthe present value of the pole pole/ig determined in STEP24-5 inSTEP24-6. The coefficient parameters s3, s4 in the equation (39) are“1”, “pole/ig”, respectively.

Then, the ignition timing control means 26 determines the equivalentcontrol input DIGeq, the reaching law input DIGrch, and the adaptive lawinput DIGadp in the present control cycle according to the equations(42) through (44) in STEP24-7.

More specifically, for determining the equivalent control input DIGeq,the ignition timing control means 26 determines differences of thetarget rotational speeds ne/fire(k), ne/fire(k+1), which have beendetermined in STEP23-4 in the present control cycle, and the targetrotational speed ne/fire(k−1), which has been determined in STEP23-4 inthe preceding control cycle, from the reference rotational speed Ne0(=the idling rotational speed NOBJ), i.e., determines the differencerotational speeds dne(k), dne(k+1), dne(k−1). The ignition timingcontrol means 26 then calculates the equation (42) to determine theequivalent control input DIGeq(k), using the difference rotationalspeeds dne(k), dne(k+1), dne(k−1), the rotational speed differencesEn(k), En(k−1) determined in STEP23-8 in the present and precedingcontrol cycles, and the present value of the pole pole/ig determined inSTEP24-5. The coefficient parameters s3, s4 in the equation (42) are“1”, “pole/ig”, respectively. The model parameters c1, c2, d1 in theequation (42) are of predetermined values identified in advance withrespect to the rotational speed controlled model (see the equation(38)).

For determining the reaching law input DIGrch, the ignition timingcontrol means 26 calculates the equation (43) using the value of theswitching function o2(k) determined in STEP24-6 to determine thereaching law input DIGrch(k). The coefficient parameter s3 in theequation (43) is “1”, and the coefficient F3 in the equation (43) is avalue preset to satisfy the condition of the equation (45) or (45)′.

For determining the adaptive law input DIGadp, the ignition timingcontrol means 26 accumulates the value of the switching function σ2determined in each control cycle in STEP24-6 in successive controlcycles to determine an integrated value Σσ2 of the switching functionσ2. Using the integrated value Σσ2, the ignition timing control means 26calculates the equation (44) to determine the adaptive law input DIGadp.The coefficient parameter s3 in the equation (44) is “1”, and thecoefficient F4 in the equation (44) is a value preset to satisfy thecondition of the equation (46).

After having determined the equivalent control input DIGeq, the reachinglaw input DIGrch, and the adaptive law input DIGadp in the mannerdescribed above, the ignition timing control means 26 calculates theirsum according to the equation (41) thereby to determine the ignitiontiming difference command value DIG(k) in the present control cycle inSTEP24-8. Thereafter, control goes back to the subroutine shown in FIG.23.

In FIG. 23, after having calculated the ignition timing differencecommand value DIG(k) in STEP23-12, the ignition timing control means 26limits the value of the ignition timing difference command value DIG(k)to a value between predetermined upper and lower limit values (whenDIG(k)>the upper limit value or DIG(k)<the lower limit value, theignition timing control means 26 forcibly limits DIG(k) to the upperlimit value and the lower limit value, respectively) in STEP23-13. Then,control returns to the subroutine shown in FIG. 22.

If f/fpause=1 in STEP23-9, i.e., if the FIRE mode is to be interrupted,then the ignition timing control means 26 interrupts the ignition timingcontrol rotational speed F/B control process. In order to return thecommand value iglog for the ignition timing gradually to the basiccommand value igbase, i.e., to return the ignition timing differencecommand value DIG gradually to “0”, the ignition timing control means 26determines a unit value dec/ig for defining the amount by which thecommand value iglog is to be returned in each control cycle (>0,hereinafter referred to as an “ignition timing returning unit valuedec/ig”) in STEP23-14.

If f/fireon=0 in STEP23-1, i.e., if the FIRE mode is to be ended or notto be carried out, then the ignition timing control means 26 determinesan ignition timing returning unit value dec/ig in order to return thecommand value iglog for the ignition timing gradually to the basiccommand value igbase in STEP23-15.

In STEP23-15, the ignition timing returning unit value dec/ig is set toa predetermined value (constant value). The ignition timing returningunit value dec/ig established in STEP23-14 for interrupting the FIREmode is determined to be a value proportional to the present opening ofthe throttle valve 5 (the ignition timing returning unit value dec/iggreater as the opening of the throttle valve 5 is greater).

The reason for the above ignition timing returning unit value dec/ig isas follows: The FIRE mode is interrupted basically when the acceleratorpedal of the vehicle is depressed to run the vehicle or race theinternal combustion engine 1. At this time, the opening of the throttlevalve 5 is controlled at the opening depending o the acceleratormanipulated quantity Ap. When the opening of the throttle valve 5 islarge, it is preferable to return the ignition timing as quickly aspossible to a normal ignition timing (which corresponds to the basiccommand value igbase) in order to keep a desired power output capabilityof the internal combustion engine 1. In STEP23-14, therefore, theignition timing returning unit value dec/ig is determined to be a valueproportional to the opening of the throttle valve 5.

The opening command given from the controller to the throttle valveactuator 23 or the detected value of the opening by a sensor (not shown)is used as the opening of the throttle valve 5 which is required todetermine the ignition timing returning unit value dec/ig.

After having determined the ignition timing returning unit value dec/ig,the ignition timing control means 26 then determines whether the presentvalue of the ignition timing difference command value DIG (which is theignition timing difference command value DIG(k−1) determined in thepreceding control cycle) is smaller than “0” or not, i.e., whether thepresent value of the ignition timing difference command value DIG is aretarded value or not, in STEP24-16.

If DIG(k−1)<0, i.e., if DIG(k−1) is of a retarded value, then theignition timing control means 26 determines the sum (DIG(k−1)+dec/ig) ofthe present ignition timing difference command value DIG(k−1) and theignition timing returning unit value dec/ig determined in STEP24-14 or24-15 as an ignition timing difference command value DIG(k) in thepresent control cycle in STEP24-17. Then, control returns to thesubroutine shown in FIG. 22. The upper limit for the ignition timingdifference command value DIG(k) is set to “0”, and if (DIG(k−1)+dec/ig)is greater than “0”, then the value of the ignition timing differencecommand value DIG(k) is forcibly set to “0”.

If DIG(k−1)≧0 (essentially DIG(k−1)=0) in STEP24-16, then the ignitiontiming control means 26 determines the value of the FIRE mode executionon/off flag f/fireon in STEP24-18. If f/fireon=1 (the FIRE mode is beinginterrupted), then the ignition timing control means 26 sets theignition timing difference command value DIG(k) in the present controlcycle to “0” in STEP24-19, after which control returns to the subroutineshown in FIG. 22.

While the FIRE mode is being interrupted (f/fireon=1 and f/fpause=1),the value of the integrated value Σσ2 of the switching function σ2 isheld as the value immediately prior to the interruption of the FIREmode.

If f/fireon=0 in STEP24-18, i.e., if the FIRE mode is ended, then theignition timing control means 26 resets the values of the FIREinterruption flag f/fpause and the rotational speed F/B execution on/offflag f/nefb to “0”, and initializes the ignition timing differencecommand value DIG(k), the value of the switching function σ2 and itsintegrated value Σσ2, the value of the equivalent control input DIGeq,the value of the reaching law input DIGrch, and the value of theadaptive law input DIGadp to “0” in STEP24-20. Thereafter, controlreturns to the sub-routine shown in FIG. 22.

In FIG. 22, after having determined the ignition timing differencecommand value DIG in STEP22-2, the ignition timing control means 26 addsthe ignition timing difference command value DIG determined in STEP22-2to the basic command value igbase determined in STEP22-1 for therebydetermining a command value iglog for the ignition timing in the presentcontrol cycle in STEP22-3.

Then, the ignition timing control means 26 determines the retarded limitvalue IGLGG for the ignition timing and the threshold value IGX that isslightly more advanced than the retarded limit value IGLGG as shown inFIG. 12 with respect to the ignition-timing-dependent correcting processcarried out by the intake air quantity control means 25 in STEP22-4.

The retarded limit value IGLGG for the ignition timing is determinedfrom the engine temperature Tw based on a data table (not shown) suchthat the internal combustion engine 1 can operate normally with advancedignition timing greater than the retarded limit value IGLGG. Thethreshold value IGX is set to a value which is the sum of the retardedlimit value IGLGG and a predetermined value (constant value), i.e., avalue which is more advanced than the retarded limit value IGLGG by apredetermined value. The retarded limit value IGLGG is a constant valueinsofar as the engine temperature Tw is in a normal temperature range,but more advanced than in the normal temperature range insofar as theengine temperature Tw is in a considerably low temperature range.

After having determined the retarded limit value IGLGG for the ignitiontiming and the threshold value IGX, the ignition timing control means 26compares the command value iglog determined in STEP22-3 with thethreshold value IGX in STEP22-5. If the command value iglog is equal toor more advanced than the threshold value IGX (iglog≧IGX), then sincethe ignition-timing-dependent correcting process is not carried out, theignition timing control means 26 sets the value of the ignition timingdetermining flag f/dec (see STEP15-7 shown in FIG. 15) to “0” inSTEP22-6, after which control goes to STEP22-11.

If iglog<IGX in STEP22-5, the ignition timing control means 26 sets thevalue of the ignition timing determining flag f/dec to “1” in order tocarry out the ignition-timing-dependent correcting process in STEP22-7.Then, the ignition timing control means 26 determines the value of thelearning calculation end flag f/flrnend relative to the learningcalculation process carried out by the intake air quantity control means25 in STEP22-8. Only if f/flrnend=0, the ignition timing control means26 holds the present value of the FIRE elapsed time t/fire as the valueof the learning end time parameter t/kil in STEP22-9. Then, the ignitiontiming control means 26 sets the value of the learning calculation endflag f/flrnend to “1” in order to end the calculation of the basiclearning corrective coefficient vpskisld in STEP22-10.

Then, the ignition timing control means 26 compares the command valueiglog determined in STEP22-3 with the retarded limit value IGLGGdetermined in STEP22-4 in STEP22-11. If iglog≧IGLGG, i.e., if thecommand value iglog falls within the retarded limit value IGLGG, thencontrol returns to the main routine shown in FIG. 4.

If iglog<IGLGG, i.e., if the command value iglog determined in STEP22-3is more retarded than the retarded limit value IGLGG, then the ignitiontiming control means 26 forcibly sets the command value iglog to theretarded limit value IGLGG in STEP22-12. The ignition timing controlmeans 26 holds the integrated value Σσ2 of the switching function σ2forcibly as the value determined in the control cycle immediately beforeiglog<IGLGG in STEP22-13. Thereafter, control returns to the mainroutine shown in FIG. 4. The integrated value Σσ2 is held because if thecalculation of the ignition timing difference command value DIG werecontinued by the processing in STEP23-12 with the command value iglogfor the ignition timing being forcibly set to the limit value IGLGG, theintegrated value Σσ2 of the switching function σ2 and hence the value(absolute value) of the adaptive law input DIGadp would excessively belarge.

The processing described above with reference to FIGS. 19 through 24 isa detailed process for generating the command value iglog for theignition timing in STEP4-6 shown in FIG. 4. The command value iglog thusgenerated is given to the ignition unit 21, which controls the ignitiontiming of the internal combustion engine 1 according to the givencommand value iglog.

According to the operation of the system described above, in the FIREmode, the amount of intake air introduced into the combustion chamber 4is increased to a level higher than in the normal idling mode bycontrolling the bypass opening. Concurrent with this, the ignitiontiming control rotational speed F/B control process controls theignition timing to be retarded so as to converge the rotational speed Neto the predetermined target rotational speed ne/fire (finally the idlingrotational speed NOBJ). Therefore, the amount of heat energy given tothe catalytic converter 3 by exhaust gases generated by the internalcombustion engine 1 upon combustion of the air-fuel mixture is madegreater than in the normal idling mode, so that it is possible toquickly increase the temperature of and activate the catalytic converter3, and at the same time to keep the rotational speed Ne which tends toincrease due to the increased amount of intake air at an appropriatelevel.

With respect to increasing the amount of intake air, the command valuefor the bypass opening is corrected by the amount-of-intake-air F/Bcontrol correcting process using the intake adaptive SLD control processin order to converge the predicted integrated amount qair/pre of intakeair corresponding to the integrated value of the amount of heat energyactually given, from instant to instant, to the catalytic converter 3after the amount of intake air has started to be increased, to thetarget integrated amount qair/cmd of intake air corresponding to thetarget integrated value of the amount of heat energy to be actuallygiven to the catalytic converter 3.

For example, as shown in a midd1 e diagram section of FIG. 25, when thepredicted integrated amount qair/pre of intake air suffers an error(intake difference Eq) with respect to the target integrated amountqair/cmd of intake air that is determined dependent on the standardopening command value θ0 because of a variation in the amount of intakeair due to structural factors, the opening command Θ (command value forthe bypass opening) is corrected by the SLD opening corrective quantityi/sld with respect to the standard opening command value θ0, as shown inan upper diagram section of FIG. 25. The correction of the openingcommand Θ is capable of converging the predicted integrated amountqair/pre of intake air to the target integrated amount qair/cmd ofintake air as shown in the midd1 e diagram section of FIG. 25, and hencecausing the integrated value of the amount of heat energy actually givento the catalytic converter 3 to follow the target value thereof. In thismanner, variations in the amount of intake air due to structural factorscan be compensated for, and hence variations in the pattern in which thetemperature of the catalytic converter 3 increases due to structuralfactors can be eliminated.

In this embodiment, furthermore, the opening command Θ is corrected byway of multiplication by the atmospheric pressure corrective coefficientkpa and the atmospheric temperature corrective coefficient kta which aredetermined by the atmospheric condition correcting process.Specifically, as the atmospheric pressure Pa is lower, the openingcommand Θ is corrected so as to be larger, and as the atmospherictemperature is higher, the opening command Θ is corrected so as to belarger. In this manner, variations in the amount of intake air due toatmospheric conditions can be compensated for, and hence variations inthe pattern in which the temperature of the catalytic converter 3increases due to atmospheric conditions can be eliminated.

As a result, the pattern of the temperature increase of the catalyticconverter 3 in the FIRE mode can be brought into conformity with adesired pattern (in this embodiment, if the engine temperature Tw andthe shifted position of the automatic transmission while in the FIREmode are constant, then the pattern of the temperature increase of thecatalytic converter 3 in each FIRE mode is substantially the same exceptwhen the FIRE mode is interrupted), and the catalytic converter 3 canreliably be increased in temperature and activated in the FIRE mode.

Since the standard opening command value θ0, the target amount gair/cmdof intake air, and the target integrated amount qair/cmd of intake airare established so as to be dependent on the engine temperature Tw atthe start of the internal combustion engine 1, which corresponds to thetemperature status of the catalytic converter 3 at the start of theinternal combustion engine 1 (basically, as the engine temperature Tw ishigher, the target amount gair/cmd of intake air and the targetintegrated amount qair/cmd of intake air are smaller), the catalyticconverter 3 can be increased in temperature and activated in a manner tomatch the temperature status of the catalytic converter 3 at the startof the internal combustion engine 1. Specifically, the pattern of thetemperature increase of the catalytic converter 3 in the FIRE mode (thetimedependent degree of increase of the temperature) depends on thetemperature status of the catalytic converter 3 at the start of theinternal combustion engine 1, and the final temperature status of thecatalytic converter 3 in the FIRE mode can be made optimum for theactivation of the catalytic converter 3.

The target integrated amount qair/cmd of intake air defined by thestandard opening command value θ0 is established such that the amount ofintake air to be drawn into the combustion chamber 4 dependent thereonin each control cycle, i.e., the target amount gair/cmd of intake air,is gradually reduced after the FIRE elapsed time t/fire has reached thepredetermined value t2 (see FIG. 7), i.e., after the internal combustionengine 1 has been warmed up to a certain extent. Therefore, even if thefriction of various components of the internal combustion engine 1 isreduced as the internal combustion engine 1 is warmed up, the rotationalspeed Ne is prevented from tending to increase. As a result, theignition timing of the internal combustion engine 1 is prevented frombeing excessively retarded by the ignition timing control rotationalspeed F/B control process.

Furthermore, when the command value iglog for the ignition timingdetermined by the ignition timing control rotational speed F/B controlprocess exceeds the threshold value IGX close to the retarded limitvalue IGLGG for the ignition timing, the amount-of-intake-air F/Bcontrol correcting process is interrupted, and the opening command Θ isreduced in a feed-forward manner by the ignition-timing-dependentcorrecting process. Therefore, even if the friction of the internalcombustion engine 1 is lowered to a degree greater than expected orlowered quickly, it is possible to reduce an increase in the tendency ofthe rotational speed Ne to increase, and to prevent the ignition timingfrom being excessively retarded until it would reach the retarded limitvalue IGLGG.

In the present embodiment, the amount-of-intake-air F/B controlcorrecting process employs the sliding mode control process which isless susceptible to disturbances and errors in the modeling of theobject to be controlled, particularly the adaptive sliding mode controlprocess (the intake adaptive SLD control process) which uses theadaptive law for eliminating the effect of disturbances, etc. as much aspossible, for highly stably converging the predicted integrated amountqair/pre of intake air to the target integrated amount qair/cmd ofintake air and hence converging the integrated value of the amount ofheat energy given to the catalytic converter 3 to its target value. As aconsequence, the catalytic converter 3 can more reliably be increased intemperature and activated.

In the intake adaptive SLD control process of the amount-of-intake-airF/B control correcting process, the object to be controlled thereby isconsidered to be a system for generating the integrated amount Qa ofintake air from the opening command Θ, and is expressed by adiscrete-system model (intake-side controlled model). Therefore, thealgorithm of the ignition timing adaptive SLD control process can beconstructed more simply and suitable for computer processing than if theobject to be controlled were expressed by a continuous-system model.

Because the object to be controlled by the intake adaptive SLD controlprocess is expressed as a discrete-system model, the switching functionσ1 used in the intake adaptive SLD control process can be constructedusing time-series data of only the intake difference Eq without usingthe rate of change of the intake difference Eq. As a result, thereliability of the value of the switching function σ1 required todetermine the SLD opening corrective quantity i/sld can be increased,and hence the reliability of the intake adaptive SLD control process canbe increased.

In the intake adaptive SLD control process, by omitting the feedbackterm Θeq/fb of the equivalent control input Θeq and employing thestandard opening command value θ0 corresponding to the feed-forward termΘeq/ff as the equivalent control input Θeq in this embodiment, the SLDopening corrective quantity i/sld can be determined by a simplealgorithm without using the model parameters a1, a2, b1 of the model tobe controlled (the intake controlled model).

While the SLD opening corrective quantity i/sld can be determined usingthe model parameters a1, a2, b1, since the model to be controlled by theintake adaptive SLD control process is constructed by a discrete system,the values of the model parameters a1, a2, b1 can accurately beidentified by using a known identifying algorithm.

In the amount-of-intake-air F/B control correcting process, as shown inthe midd1 e diagram section of FIG. 25, until the SLD correction limittime TISLDLMT elapses immediately after the start of the internalcombustion engine 1 elapses, the values of the predicted integratedamount qair/pre of intake air and the target integrated amount qair/cmdof intake air are forcibly held to “0”, and the value of the SLD openingcorrective quantity i/sld is also held to “0”.

Therefore, immediately after the start of the internal combustion engine1, the amount-of-intake-air F/B control correcting process is notperformed until the SLD correction limit time TISLDLMT elapses, and thebypass opening is controlled in a feed-forward manner primarily based onthe standard opening command value θ0 (more accurately, the valueproduced by multiplying the standard opening command value θ0 by theatmospheric pressure corrective coefficient kpa, the atmospherictemperature corrective coefficient kta, and the learning correctivecoefficient kilearn (see the upper diagram section of FIG. 25).

Accordingly, immediately after the start of the internal combustionengine 1, the amount of intake air is smoothly increased in the samepattern as the pattern of increase of the standard opening command valueθ0, with the result that the combustion status of the internalcombustion engine 1 is smoothly stabilized immediately after it hasstarted, thereby achieving a good emission status of the internalcombustion engine 1.

For actually starting the amount-of-intake-air F/B control correctingprocess, the value of the pole pole/i relative to the intake adaptiveSLD control process is gradually increased from “−1” (|pole/i| isgradually reduced) until the FIRE elapsed time t/fire reaches thepredetermined value TPOLEX, as shown in a lower diagram section of FIG.25, so that the rate of reduction of the intake difference Eq is madesmaller until the FIRE elapsed time t/fire reaches the predeterminedvalue TPOLEX than after the FIRE elapsed time t/fire has reached thepredetermined value TPOLEX.

As a consequence, when the amount-of-intake-air F/B control correctingprocess is started, the opening command Θ and hence the amount of intakeair are prevented from greatly varying abruptly, so that the stabilityof the combustion status of the internal combustion engine 1 can bemaintained in an initial stage after its start while achieving a goodemission status of the internal combustion engine 1.

In this embodiment, furthermore, according to the learning correctingprocess, the SLD opening corrective quantity i/sld produced by theamount-of-intake-air F/B control correcting process is learned, and thelearning corrective coefficient kilearn (basically the basic learningcorrective coefficient vpskisld) based on the value of the ratio of theSLD integrated intake corrective quantity qair/sld produced byintegrating the SLD opening corrective quantity i/sld in the FIRE mode,to the target integrated amount qair/cmd of intake air is determined.For a next FIRE mode, the opening command Θ is corrected by beingmultiplied by the learning corrective coefficient kilearn in afeed-forward fashion in the full period of the FIRE mode, so that anycorrection of the opening command Θ in each control cycle based on theSLD opening corrective quantity i/sld in the FIRE mode can be held to aminimum. As a result, even if the amount of intake air varies greatlydue to structural factors, the pattern of timedependent changes of theamount of intake air is prevented from largely deviating from thepattern of the standard opening command value θ0, and the internalcombustion engine 1 can be operated stably without impairing thecombustion and emission statuses of the internal combustion engine 1.

In this embodiment, even when the vehicle is propelled or the internalcombustion engine 1 is raced by depressing the accelerator pedal in theFIRE mode, and the internal combustion engine 1 operates in a mode otherthan the idling mode, resulting in interrupting the FIRE mode, thebypass opening is controlled to increase the amount of intake air (theamount-of-intake-air F/B control correcting process is interrupted), andthe calculation of the predicted integrated amount qair/pre of intakeair and the target integrated amount qair/cmd of intake air iscontinued. After the interruption of the FIRE mode is canceled, theamount-of-intake-air F/B control correcting process is resumed, and theopening command Θ is corrected to converge the predicted integratedamount qair/pre of intake air to the target integrated amount qair./cmdof intake air. Therefore, when the internal combustion engine 1 operatesin a mode other than the idling mode while in the FIRE mode, resultingin interrupting the FIRE mode, the catalytic converter 3 can reliably beincreased in temperature and activated within the FIRE mode limit timeTFIRELMT.

With respect to the ignition timing control rotational speed F/B controlprocess, the feedback control process thereof employs the adaptivesliding mode control process (the ignition timing adaptive SLD controlprocess) as with the amount-of-intake-air F/B control correctingprocess, for thereby increasing the stability of converging therotational speed Ne to the target rotational speed ne/fire.

At this time, based on the response designating characteristics of theignition timing adaptive SLD control process which is a responsedesignating control process, the ignition-timing-dependent pole basicvalue pole/igtbl which is established as a normal value for the polepole/ig (=s4/s3) which defines the rate of reduction of the rotationalspeed difference En (=Ne−ne/fire) is variably determined such that asthe command value iglog for the ignition timing that is controlled forthe control of the rotational speed Ne is more retarded, the rate ofreduction of the rotational speed difference En is reduced. Generally,as the ignition timing is more retarded, a change in the rotationalspeed Ne with respect to a change in the ignition timing is greater.Under such a condition, the value of the pole pole/ig is established soas to reduce the rate of reduction of the rotational speed difference Enfor thereby suppressing the change in the command value iglog determinedby the ignition timing adaptive SLD control process to prevent therotational speed Ne from changing abruptly with respect to the targetrotational speed ne/fire. If the ignition timing is advanced, the valueof the pole pole/ig is established so as to increase the rate ofreduction of the rotational speed difference En for thereby enabling therotational speed Ne to follow the target rotational speed ne/firequickly. Consequently, the process of controlling the rotational speedNe at the target rotational speed ne/fire can be performed quickly andstably.

In an initial stage immediately after the ignition timing controlrotational speed F/B control process has started, i.e., until therotational speed F/B elapsed time Δt/nfb reaches the predetermined valueT/NFBX, the ignition-timing-dependent pole basic value pole/igtbl iscorrected by being multiplied by the time-dependent correctivecoefficient kigt to determine the pole pole/ig in order to reduce therate of reduction of the rotational speed difference En. In thisfashion, the rotational speed Ne is prevented from varying abruptlyimmediately after the start of the ignition timing control rotationalspeed F/B control process, so that the combustion status of the internalcombustion engine 1 is prevented from being impaired.

In the present embodiment, when the ignition timing control rotationalspeed F/B control process is resumed after the interruption of the FIREmode is canceled, the ignition-timing-dependent pole basic valuepole/igtbl is corrected by being multiplied by therotational-speed-dependent corrected corrective coefficient kignef todetermine the pole pole/ig in order to reduce the rate of reduction ofthe rotational speed difference En as the rotational speed Ne is muchhigher than the target rotational speed ne/fire. In this manner, whenthe rotational speed Ne is much higher than the target rotational speedne/fire at the time of resuming the ignition timing control rotationalspeed F/B control process, the command value iglog for the ignitiontiming is prevented from abruptly becoming retarded depending on thelarge rotational speed difference En, and the internal combustion engine1 can operate stably.

Furthermore, the absolute value of the pole pole/ig for defining therate of reduction of the rotational speed difference En relative to theamount-of-intake-air F/B control correcting process is established so asto be greater than the absolute value of the pole pole/ig for definingthe rate of reduction of the rotational speed difference En relative tothe ignition timing control rotational speed F/B control process (seethe processing in STEP17-7, STEP17-8 shown in FIG. 17). Statedotherwise, the pole pole/ig is set to such a value that the rate ofreduction of the rotational speed difference En is higher than the rateof reduction of the intake difference Eq. Consequently, the feedbackcontrol process for converging the rotational speed Ne to the targetrotational speed ne/fire according to the ignition timing controlrotational speed F/B control process and the feedback control processfor converging the predicted integrated amount qair/pre of intake air tothe target integrated amount qair/cmd of intake air according to theamount-of-intakeair F/B control correcting process are prevented frominterfering with each other thereby to controlling the rotational speedNe stably at the target rotational speed ne/fire.

In the ignition timing adaptive SLD control process used in the ignitiontiming control rotational speed F/B control process, the object to becontrolled thereby is considered to be a system for generating thedifference rotational speed DNE corresponding to the rotational speed Nefrom the ignition timing difference command value DIG corresponding tothe command value iglog for the ignition timing and is expressed by adiscrete-system model (rotational speed controlled model). Therefore,the algorithm of the ignition timing adaptive SLD control process can beconstructed simply and suitable for computer processing.

Because the object to be controlled by the intake adaptive SLD controlprocess is expressed as a discrete-system model, the switching functionσ2 can be constructed using time-series data of only the intakedifference Eq without using the rate of change of the rotational speeddifference En, as with the intake adaptive SLD control process. As aresult, the reliability of the value of the switching function σ2required to determine the ignition timing difference command value DIGcan be increased, and hence the reliability of the ignition timingadaptive SLD control process can be increased.

In the above embodiment, while the internal combustion engine is idlingafter it has started to operate, the rotational speed Ne is converged tothe target rotational speed ne/fire according to the ignition timingcontrol rotational speed F/B control process while the amount of intakeair is being increased. However, the present invention is alsoapplicable to a process in which the amount of intake air is notincreased and the ignition timing is controlled by a feedback controlprocess to converge the rotational speed Ne to a certain targetrotational speed Ne.

In the above embodiment, the pole pole/ig which defines the rate ofreduction of the rotational speed difference En is variably establisheddepending on the command value iglog for the ignition timing, therotational speed F/B elapsed time Δt/nfb, and the rotational speed Ne.However, the pole pole/ig may be variably established depending onsuitable conditions in view of the controllability of the rotationalspeed Ne at the target rotational speed and the stability of theoperating conditions of the internal combustion engine 1.

In the illustrated embodiment, the adaptive sliding mode control processis employed as the response designating control process of theamount-of-intake-air F/B control correcting process. However, a normalsliding mode control process free of the adaptive law may be employed.Moreover, the rate of reduction of the rotational speed difference Enmay be designated in the same manner as described in the embodiment byusing an ILQ control process (response designating optimum controlprocess).

The object to be controlled by the amount-of-intake-air F/B controlcorrecting process is expressed by a discrete-system model in theillustrated embodiment. However, it may be expressed by acontinuous-system model.

In this embodiment, with respect to the feedback control process basedon controlling the amount of intake air (controlling the bypassopening), the estimated integrated amount qair/pre of intake air ishand1 ed as a control quantity to be controlled, and the estimatedintegrated amount qair/pre of intake air is converged to the targetintegrated amount qair/cmd of intake air. However, the present inventionis also applicable to controlling the amount of intake air in order toconverge the output torque of the internal combustion engine 1 to itstarget value.

In the illustrated embodiment, the object to be controlled by theamount-of-intake-air F/B control correcting process is expressed by asecondary autoregressive model (discrete-system model). However, it maybe expressed by an autoregressive model of higher order. In this case,the switching function required for the amountof-intake-air F/B controlcorrecting process needs to be established as a linear function of threeor more time series data of the intake difference Eq, for example. Evenwith such a scheme, the rate of reduction of the intake difference Eqcan be designated by the values of coefficient parameters of theswitching function as with the illustrated embodiment. This holds truealso for the ignition timing adaptive SLD control process.

A process of designating the rate of reduction of the intake differenceEq and the rotational speed difference En in the same manner as with theillustrated embodiment if the object to be controlled by the intakeadaptive SLD control process or the ignition timing adaptive SLD controlprocess is expressed by an autoregressive model (discrete-system model)of third order will briefly be described below. In the followingdescription, the intake adaptive SLD control process and the ignitiontiming adaptive SLD control process are collectively referred to as an“adaptive SLD control process”. Input and output of an object to becontrolled by the adaptive SLD control process are referred to as X, Y,a target value for the output Y of the object to be controlled, which isa control quantity of the adaptive SLD control process, is referred toas y, and the difference between the output Y and the target value y isreferred to as E (=Y−y). With respect to the intake adaptive SLD controlprocess, the input X, the output Y (control quantity), the target valuey, and the difference E correspond respectively to the opening command Θ(command value for the bypass opening), the predicted integrated amountqair/pre of intake air, the target integrated amount qair/cmd of intakeair, and the intake difference Eq. With respect to the ignition timingadaptive SLD control process, the input X, the output Y (controlquantity), the target value y, and the difference E correspondrespectively to the ignition timing difference command value DIG(=iglog−igbase), the difference rotational speed DNE (Ne−NOBJ), thetarget difference rotational speed dne (ne/fire−NOBJ), and therotational speed difference En (=Ne−ne/fire).

The object to the controlled by the adaptive SLD control process isexpressed by an autoregressive model of third order according to thefollowing equation (52), for example, i.e., a discrete-system model inwhich the output Y of the object to be controlled in each control cycleis represented by an output Y of the object to be controlled up to threeprevious control cycles and an input X of the object to be controlled ina preceding control cycle:

Y(k+1)=e1·Y(k)+e2·Y(k−1)+e3·Y(k−2)+f1·X(k)  (52)

A switching function a3 used in the adaptive SLD control process isdefined by a linear function of three time-series data E(k), E(k−1),E(k−2) of the difference E (hereinafter referred to as a “controlquantity difference E”) between the output Y (control quantity) and thetarget value y, as represented by the following equation (53):$\begin{matrix}\begin{matrix}{{{\sigma 3}(k)} = \quad {( {{Y(k)} - {y(k)}} ) + {{s5} \cdot ( {{Y( {k - 1} )} - {y( {k - 1} )}} )} +}} \\{\quad {{s6} \cdot ( {{Y( {k - 2} )} - {y( {k - 2} )}} )}} \\{= \quad {{E(k)} + {{s5} \cdot {E( {k - 1} )}} + {{s6} \cdot {E( {k - 2} )}}}}\end{matrix} & (53)\end{matrix}$

In the equation (52), e1 through e3 and f1 represent model parameterswhich define the behavioral characteristics of the object to becontrolled. In the equation (53), s5, s6 represent coefficientparameters of the switching function σ3. The coefficient relative to thecontrol quantity difference En(k) is set to “1” for the sake of brevity.

The condition for converging (reducing) the control quantity differenceEn stably to “0” while the value of the switching function σ3 is beingconverged to “0” is that the characteristic root of the followingequation (54) obtained as σ3=0 in the equation (53), i.e., thecharacteristic roots λ1, λ2 given by the following equation (55), arepresent in a unit circle on a complex plane.

E(k)=−s5·E(k−1)−s6-·E(k−2)  (54)

$\begin{matrix}{{{\lambda 1} = \frac{{- {s5}} + \sqrt{{s5}^{2} - {4 \cdot {s6}}}}{2}}{{\lambda 2} = \frac{{- {s5}} - \sqrt{{s5}^{2} - {4 \cdot {s6}}}}{2}}} & (55)\end{matrix}$

A combination of the values of the coefficient parameters s5, s6 of theswitching function σ3 which satisfies the above condition is acombination of the values of the coefficient parameters s5, s6determined by points in an area surrounded by a triangle A1A2A3 on acoordinate plane (a coordinate plane having the coefficient parameterss5, s6 as components) shown in FIG. 26. If the values of the coefficientparameters s5, s6 are established such that a point determined therebyon the coordinate plane shown in FIG. 26 is present in the triangleA1A2A3, then it is possible to converge the control quantity differenceEn stably to “0” while the value of the switching function σ3 is beingconverged to “0”.

For converging the control quantity difference E in a non-oscillatoryfashion to “0”, the values of the coefficient parameters s5, s6 may beestablished such that a point on the coordinate plane shown in FIG. 26is present in a stippled area (hereinafter referred to as an “areaA1A2A4”) within the triangle A1A2A3. A curve A1A4 which defines theupper boundary of the area A1A2A4 is a parabolic curve expressed by thequadratic function s6=s5²/4. A point A4 represents the origin of thecoordinate plane.

When the values of the coefficient parameters s5, s6 are establishedsuch that a point (s5, s6) determined thereby is present within the areaA1A2A4, the rate of reduction of the control quantity difference Ebecomes greater as the point (s5, s6) approaches the origin A4 bychanging the values of the coefficient parameters s5, s6 to move thepoint (s5, s6) from the side A1A2 of the area A1A2A4 toward the originA4.

For example, when the values of the coefficient parameters s5, s6 arechanged to move the point (s5, s6) from the point A1 to the origin A4 onthe curve (parabolic curve) A1A4 (see the arrow B1 in FIG. 26), the rateof reduction of the control quantity difference E increases continuouslygradually.

Alternatively, for example, when the values of the coefficientparameters s5, s6 are changed to move the point (s5, s6) from the sideA1A2 of the area A1A2A4 to the origin A4 on a straight line expressed bythe equation s6=η·s5 (η>0) (see the arrow B2 in FIG. 26), the rate ofreduction of the control quantity difference E increases continuouslygradually.

With respect to the ignition timing adaptive SLD control process of theignition timing control rotational speed F/B control process, in orderto reduce the rate of reduction of the rotational speed difference En asthe command value iglog for the ignition timing is more retarded, thevalues of the!coefficient parameters s5, s6 may be variably establisheddepending on the command value iglog for the ignition timing such thatthe point (s5, s6) moves within the area A1A2A4 toward the side A1A2(away from the origin A4) as the command value iglog for the ignitiontiming is more retarded. The coefficient parameters s5, s6 may similarlybe variably established for reducing the rate of reduction of therotational speed difference En as the rotational speed difference En isgreater (as the rotational speed Ne is much higher than the targetrotational speed ne/fire), and for reducing the rate of reduction of therotational speed difference En until the rotational speed F/B elapsedtime Δt/nfb reaches the predetermined value T/NFBX, when the ignitiontiming control rotational speed F/B control process is reduced by thecancellation of the interruption of the FIRE mode.

In this case, for variably establishing the coefficient parameters s5,s6, the point (s5, s6) is preferably moved on the curve (parabolic curves6=s5²/4) A1A4 or on the straight line s6=η·s5. With this arrangement,if either one of the coefficient parameters s5, s6 is establisheddepending on the command value iglog for the ignition timing, therotational speed Ne, and the rotational speed F/B elapsed time Δt/nfb,then the value of the other coefficient parameter is determined, andhence it is easier to variably establish the coefficient parameters s5,s6.

More specifically, if the point (s5, s6) is to move on the curve(parabolic curve s6=s5²/4) A1A4, basic values of the coefficientparameters s5, s6 are determined depending on the command value iglogfor the ignition timing in the same tendency as theignition-timing-dependent pole basic value pole/igtbl (see FIG. 20)within a range−2<s5<0 (“−2”, “0” are lower and upper limit values,respectively, of the coefficient parameter s5 on the curve A1A4 of thearea A1A2A4). The basic value of the coefficient parameter s5 ismultiplied by a corrective coefficient determined depending on therotational speed F/B elapsed time Δt/nfb in the same tendency as thetime-dependent corrective coefficient kigt and a corrective coefficientdetermined dependent on the rotational speed Ne in the same tendency asthe rotational-speed-dependent corrective coefficient kigne (morepreferably, the rotational-speed-dependent corrected correctivecoefficient kignef) to produce a value, which is established as thevalue of the coefficient parameter s5. The coefficient parameter s6 isthen determined from the coefficient parameter s5 according to theequation s6=s5²/4. The coefficient parameters s5, s6 may similarly beestablished when the point (s5, s6) is moved on the straight lines6=η·s5.

An equation for calculating the equivalent control input DIGeq requiredto determine the ignition timing difference command value DIG can bedetermined from a condition σ3(k+1)=σ3(k) and the equation (52). Thereaching law input DIGrch and the adaptive law input DIGadp may be madeproportional to the value of the switching function σ3 and itsintegrated value, as with the previous embodiment.

With respect to the intake adaptive SLD control process of theamount-of-intake-air F/B control correcting process, as with theprevious embodiment, in order to increase the rate of reduction of theintake difference Eq gradually from a low rate depending on the FIREelapsed time t/fire in an initial stage of the FIRE mode (immediatelyafter the internal combustion engine 1 has started), the values of thecoefficient parameters s5, s6 may be changed to move the point (s5, s6)from a point within the area A1A2A4 near the side A1A2 to the origin A4as the FIRE elapsed time t/fire increases.

For variably establishing the coefficient parameters s5, s6, when thepoint (s5, s6) is moved on the curve (parabolic curve s6=s5²/4) A1A4 oron the straight line s6=η·s5, it is easier to variably establish thecoefficient parameters s5, s6, as with the ignition timing adaptive SLDcontrol process.

In this case, the reaching law input Θrch and the adaptive law inputΘadp required to determine the SLD opening corrective quantity i/sld maybe made proportional respectively to the value of the switching functionσ3 and its integrated value. The standard opening command value θ0 maybe used instead of the equivalent control input Θeq.

In the above embodiment, if the air-fuel ratio of the air-fuel mixtureto be combusted in the combustion chamber 4 is constant, then since theamount of heat energy generated by the internal combustion engine 1 (theamount of heat energy of exhaust gases), and hence the amount of heatenergy given to the catalytic converter 3 are substantially proportionalto the amount of intake air introduced into the combustion engine 4, theintegrated amount of intake air in each control cycle is used as datarepresenting the amount of heat energy given to the catalytic converter3. However, inasmuch as the amount of heat energy generated by theinternal combustion engine 1 slightly varies depending on the ignitiontiming of the internal combustion engine 1, if the accuracy of the datarepresenting the amount of heat energy given to the catalytic converter3 is to be increased, then the predicted or detected value of the amountof intake air from instant to instant (in each control cycle) may becorrected dependent on the ignition timing from instant to instant, andintegrated to acquire data representing the amount of heat energy. Ifthe air-fuel ratio of the air-fuel mixture needs to be changed, then thepredicted or detected value of the amount of intake air from instant toinstant (in each control cycle) may be corrected dependent on theair-fuel ratio from instant to instant, and integrated to acquire datarepresenting the amount of heat energy. At any rate, it is possible tocarry out these processes by preparing data tables of correctivecoefficients for correcting the predicted or detected value of theamount of intake air depending on the ignition timing or the air-fuelratio.

The above correcting processes for acquiring data representing theamount of heat energy given to the catalytic converter 3 are alsoapplicable to instances where the amount of supplied fuel or otherparameters are used as the data representing the amount of heat energy.

Although certain preferred embodiments of the present invention havebeen shown and described in detail, it should be understood that variouschanges and modifications may be made therein without departing from thescope of the appended claims.

What is claimed is:
 1. An apparatus for controlling the rotational speedof an internal combustion engine by generating a command value forignition timing of the internal combustion engine to convert an actualrotational speed of the internal combustion engine to a predeterminedtarget rotational speed according to a feedback control process andcontrolling the ignition timing based on the generated command value,wherein said feedback control process is carried out by a responsedesignating control process capable of variably designating a rate ofreduction of the difference between the actual rotational speed of theinternal combustion engine and the target rotational speed with thevalue of a predetermined parameter in the feedback control process, andthe value of the predetermined parameter is variably established under apredetermined condition.
 2. An apparatus according to claim 1, whereinsaid predetermined condition for variably establishing the value of thepredetermined parameter includes the ignition timing of said internalcombustion engine controlled based on the command value for the ignitiontiming, said value of the predetermined parameter being established suchthat as the ignition timing is more retarded, the rate of reduction ofthe difference between the actual rotational speed of the internalcombustion engine and the target rotational speed is smaller.
 3. Anapparatus according to claim 1, wherein said predetermined condition forvariably establishing the value of the predetermined parameter includesthe actual rotational speed of said internal combustion engine, saidvalue of the predetermined parameter being established such that as theactual rotational speed is more different from the target rotationalspeed, the rate of reduction of the difference between the actualrotational speed of the internal combustion engine and the targetrotational speed is smaller.
 4. An apparatus according to claim 1,wherein the ignition timing of said internal combustion engine iscontrolled based on the command value for the ignition timing which isgenerated by said feedback control process, immediately after saidinternal combustion engine has started to operate while said internalcombustion engine is idling, and said predetermined condition forvariably establishing the value of the predetermined parameter includesa time which has elapsed after the ignition timing has started to becontrolled by said command value, said value of the predeterminedparameter being established such that until the elapsed time reaches apredetermined value, the rate of reduction of the difference between theactual rotational speed of the internal combustion engine and the targetrotational speed is smaller than after the elapsed time has reached thepredetermined value.
 5. An apparatus according to claim 1, comprisingamount-of-intake-air control means for controlling the amount of intakeair introduced into said internal combustion engine to converge acontrol quantity, other than the actual rotational speed, of saidinternal combustion engine to a predetermined target value according toa feedback control process, concurrent with controlling the ignitiontiming of said internal combustion engine based on the command value forthe ignition timing which is generated by said feedback control process,said value of the predetermined parameter being established such thatthe rate of reduction of the difference between the actual rotationalspeed of the internal combustion engine and the target rotational speedaccording to said response designating control process is greater thanthe rate of reduction of the difference between the control quantity andthe target value according to the feedback control process of saidamount-of-intake-air control means.
 6. An apparatus according to any oneof claims 1 through 5, wherein said response designating control processhas an object to be controlled which is hand1 ed as a system forgenerating data representing the actual rotational speed of saidinternal combustion engine from data representing the command value forsaid ignition timing, and carries out said feedback control process in apredetermined control cycle based on a discrete-system model whichrepresents a model of said object to be controlled as a discrete system.7. An apparatus according to claim 6, wherein said discrete-system modelcomprises a model in which the data representing the actual rotationalspeed of said internal combustion engine in each control cycle of saidresponse designating control process is expressed by data representingthe actual rotational speed of said internal combustion engine in acontrol cycle prior to the control cycle and data representing thecommand value for said ignition timing.
 8. An apparatus according toclaim 6, wherein said data representing the command value for saidignition timing comprises the difference between the command value forsaid ignition timing and a predetermined reference command value, andsaid data representing the actual rotational speed of said internalcombustion engine comprises the difference between said actualrotational speed and a predetermined reference rotational speed.
 9. Anapparatus according to any one of claims 1 through 5, wherein saidresponse designating control process comprises a sliding mode controlprocess.
 10. An apparatus according to claim 9, wherein said slidingmode control process comprises an adaptive sliding mode control process.11. An apparatus according to claim 9, wherein said predeterminedparameter comprises a coefficient parameter of a linear switchingfunction used in said sliding mode control process.